The method finds local minima over closed and bounded convex sets.
When the Program is convex then the minimum becomes the Global minimum. Notice that the objective is 2x1^2+x2^2+2*x1*x2 -10x1-10x2 and the graph shows the level curves and the constraints.
For the wiser few be advised to solve this problem using conditioned derivatives over decision and state variables.
The Hessian mtx tells us the function is positive definite as all minor minors are positive and we are minimizing and all constraints in first quadrant are convex so the program is convex.
The free minimum lies over point x1=0 , x2=5 .
Notice I forgot a square in a(3,1) of Jacobian mtx, but it does not affect at any calculations.
Former P.Wolfe method includes all m greatest constraints in the basis at once so that when the basis changes you need to apply m- pivot iterations on the tableaux. The rule in constructing the gradients is also modified. Best Regards.
J. Abadie, “The GRG method for non-linear programming,” in Design and Implementation of Optimization Software, H. J. Greenberg, Ed., Sijthoff and Noordhoff, Alphen aan den Rijn, The Netherlands, 1978.
D. Gabay and D. G. Luenberger, “Efficiently converging minimization methods based on the reduced gradient,” SIAM Journal on Control and Optimization, vol. 14, no. 1, pp. 42–61, 1976.
E. P. de Carvalho, A. dos Santos Jr., and T. F. Ma, “Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem,” Applied Mathematics and Computation, vol. 200, no. 2, pp. 529–536, 2008.

Views: 1939
JOAQUIN PELFORT VAZQUEZ

When Machine Learning Meets Robust Optimization: Data-driven Adaptive Robust Optimization Models, Algorithms & Applications
In this presentation, we will introduce a novel data-driven adaptive robust optimization framework that organically integrate machine learning techniques with optimization under uncertainty methods. We first propose a data-driven nonparametric uncertainty model could automatically adjust its complexity based on the data structure and complexity, thus accurately capturing the uncertainty information. The machine learning model is seamlessly integrated with adaptive robust optimization approach through a novel multi-level optimization framework. This framework explicitly accounts for the correlation, asymmetry and multimode of uncertainty data, so it generates less conservative solutions than conventional robust optimization approaches. Additionally, the proposed framework is robust not only to parameter variations, but also to data outliers. The data-driven adaptive robust optimization framework is further extended to systematically and automatically handle labeled multi-class uncertainty data through a stochastic robust optimization approach. The resulting optimization framework has a bi-level structure: The outer optimization problem follows a two-stage stochastic programming approach to optimize the expected objective across different classes of data; robust optimization is nested as the inner problem to ensure the robustness of the solution while maintaining computational tractability. Tailored column-and-constraint generation algorithms are further developed to solve the resulting multi-level optimization problem efficiently. Applications to short-term scheduling of batch processes and strategic planning of process networks are presented to demonstrate the applicability of the proposed frameworks and effectiveness of the solution algorithm.
Biography:
Fengqi You is the Roxanne E. and Michael J. Zak Professor at Cornell University, and is affiliated with Smith School of Chemical and Biomolecular Engineering, Operations Research and Information Engineering Field, Center of Applied Mathematics, and Systems Engineering Program. He earned a B.Eng. from Tsinghua University and received his Ph.D. from Carnegie Mellon University. He served on the faculty of Northwestern University from 2011 to 2016, and worked at Argonne National Laboratory as an Argonne Scholar from 2009 to 2011. He has published over 100 peer-reviewed articles in leading journals, and has an h-index of 40. Some of his research results have been editorially highlighted in Nature, featured on journal covers (e.g. Energy & Environmental Science, ACS Sustainable Chemistry & Engineering, and Industrial & Engineering Chemistry Research), and covered by major media outlets (e.g. The New York Times, BBC, BusinessWeek, and National Geographic). His recent awards (in the past five years) include Northwestern-Argonne Early Career Investigator Award (2013), National Science Foundation CAREER Award (2016), AIChE Environmental Division Early Career Award (2017), AIChE Sustainable Engineering Research Excellence Award (2017), and ACS Sustainable Chemistry & Engineering Lectureship Award (2018), as well as a number of best paper awards and most-cited article recognitions. He is currently an Associate Editor of Computers & Chemical Engineering, a Consulting Editor of AIChE Journal, and an editorial board member of several journals (e.g. ACS Sustainable Chemistry & Engineering). His research focuses on the development of novel computational models, optimization algorithms, statistical machine learning methods, and systems analysis tools for process manufacturing, smart agriculture, energy systems, and sustainability. See https://apmonitor.com/wiki/uploads/Main/2017_09_Fengqi_You.pdf Presentation recorded with WebEx.

Views: 2614
APMonitor.com

We discuss how emerging trends in computing are pushing traditionally-passive devices to perform higher level functions such data processing and predictive control. This requires of new algorithmic implementations that can operate under computing environments that are constrained by memory, power, and speed. We present a modified filter line-search algorithm that enables primal-dual regularization of the augmented system that in turn permits the use of linear algebra strategies with lower computing overheads. We prove that the proposed the algorithm is globally convergent and demonstrate the developments using a nonconvex real-time optimization application for a building heating, ventilation, and air conditioning system. Our numerical tests are performed on a standard processor and on an embedded platform and demonstrate that the approach improves solution times by up to three orders of magnitude compared to IPOPT.
Biography:
Victor M. Zavala is the Richard H. Soit Assistant Professor in the Department of Chemical and Biological Engineering at the University of Wisconsin-Madison. Before joining UW-Madison, he was a computational mathematician in the Mathematics and Computer Science Division at Argonne National Laboratory. He holds a B.Sc. degree from Universidad Iberoamericana and a Ph.D. degree from Carnegie Mellon University, both in chemical engineering. He is currently the recipient of a Department of Energy Early Career Award under which he develops scalable optimization algorithms. He is on the editorial board of the Journal of Process Control and Mathematical Programming Computation. His research interests are in the areas of mathematical modeling of energy systems, high-performance computing, stochastic optimization, and predictive control.

Views: 496
APMonitor.com

Simultaneous Contact, Gait and Motion Planning for Robust Multi-Legged Locomotion via Mixed-Integer Convex Optimization
Bernardo Aceituno-Cabezas, Carlos Mastalli, Hongka Dai, Michele Focchi, Andrea Radulescu, Darwin G. Caldwell, Jose Cappelletto, Juan Carlos Grieco, Gerardo Fernandez-Lopez, Claudio Semini
IEEE Robotics and Automation Letters (RAL), 2017
Abstract — Traditional motion planning approaches for multi-legged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or non-convex optimization with intractable computation time. In this paper, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a pre-specified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot's torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where non-convexity and flat terrain assumptions might lead to sub-optimal or unstable plans. Our method increases the motion generality while keeping a low computation time.
Official paper download link at publisher: http://ieeexplore.ieee.org/document/8141917/keywords
Pre-prints of all our papers can be found here: http://www.iit.it/hyq (Publications)
The following publications provide the details about the online computation of the terrain costmap and the whole-body controller
C. Mastalli, A. Winkler, I. Havoutis, D. G. Caldwell, C. Semini, On-line and On-board Planning and Perception for Quadrupedal Locomotion, IEEE International Conference on Technologies for Practical Robot Applications (TEPRA), 2015.
C. Mastalli, I. Havoutis, M. Focchi, D. G. Caldwell, C. Semini, Motion planning for quadrupedal locomotion: coupled planning, terrain
mapping and whole-body control, The International Journal on Robotics Research (IJRR), under-review

Views: 577
Dynamic Legged Systems lab

This video discusses primal and dual degeneracy in multi-parametric programming [by Richard Oberdieck].
Textbook on constrained optimization:
Floudas, C.A. (1995) Nonlinear and mixed-integer optimization: Fundamentals and applications. Oxford University Press.
Boyd, S.; Vandenberghe, L. (2004) Convex optimization, Cambridge University Press.
Degeneracy in multi-parametric programming:
Jones, C.N.; Baric, M.; Morari, M. (2007) Multiparametric Linear Programming with Applications to Control. European Journal of Control, 13(2-3), 152-170.
Jones, C.N.; Kerrigan, E.C.; Maciejowski, J.M. (2007) Lexicographic perturbation for multiparametric linear programming with applications to control. Automatica, 43(10), 1808-1816.

Views: 2121
Pop Toolbox

Nonparametric Analysis of Random Utility Models | Лектор: Yuichi Kitamura | Организатор: Европейский университет в Санкт-Петербурге
Смотрите это видео на Лекториуме: https://lektorium.tv/lecture/14492
This paper aims at formulating econometric tools for investigating stochastic rationality, using the Random Utility Models (RUM) to deal with unobserved heterogeneity nonparametrically. Theoretical implications of the RUM have been studied in the literature, and in particular this paper utilizes the axiomatic treatment by McFadden and Richter (McFadden and Richter, 1991, McFadden, 2005). A set of econometric methods to test stochastic rationality given a cross-sectional data is developed. This also provides means to conduct policy analysis with minimal assumptions. In terms of econometric methodology, it offers a procedure to deal with nonstandard features implied by inequality restrictions. This might be of interest on its own right, both theoretically and practically. The lecture will be held in English.
Подписывайтесь на канал: https://www.lektorium.tv/ZJA
Следите за новостями:
https://vk.com/openlektorium
https://www.facebook.com/openlektorium

Views: 772
Лекториум

Sankaran Mahadevan is Professor of Civil and Environmental Engineering at Vanderbilt University www.cee.vanderbilt.edu. Dr. Mahadevan is the director of the multidisciplinary studies (within the Civil Engineering Ph.D. program) focused on Risk and Reliability Engineering and Management. The research in Dr. Mahadevan's group is categorized into 4 areas:
1. Reliability Analysis of Structures and Materials
2. Structural Health Monitoring
3. Optimization Under Uncertainty
4. Model Uncertainty Qualification, Verification and Validation.
In this video he explains Research area #3: Optimization Under Uncertainty. Dr. Mahadevan's graduate research students Ghina Nakad, You Ling and Chen Liang also have videos on the Vanderbilt YouTube channel.
Students and Faculty pursuing multidisciplinary studies in Risk and Reliability Engineering and Management within the Civil Engineering graduate program are involved with important topics such as:
• Civil, Mechanical and Aerospace Structural Systems
• Model-Integrated Computing for Multidisciplinary Systems
• Transportation Network Systems
• Business Enterprise Systems
• Environmental Systems
• Groundwater contamination
• Atmospheric pollution
• Nuclear waste
• Electronic Devices
• Fault Detection, Isolation and Control
• Uncertainty Analysis Methods
• Time Series Modeling
• Simulation Methods
• Extreme-Value Analysis
• Evidence Theory
• Fuzzy Sets
• Bayesian Methods
• Optimization under uncertainty
• Large scale systems modeling and decision making
• Human and Organizational Systems
His comprehensive research interests are in reliability and uncertainty analysis methods, material degradation, structural health monitoring, design optimization, and model uncertainty. The methods have been applied to civil, mechanical and aerospace systems. This research has been funded by NSF, NASA (Glen, Marshall, Langley, Ames), FAA, U. S. DOE, U. S. DOT, Nuclear Regulatory Commission, U. S. Army Research Office, U.S. Air Force, U. S. Army Corps of Engineers, General Motors, Chrysler, Union Pacific, Transportation Technology Center, and the Sandia, Los Alamos, Idaho and Oak Ridge National Laboratories.
Professor Mahadevan developed and directed an NSF-IGERT multidisciplinary studies program in Reliability and Risk Engineering and Management at Vanderbilt University, which started in 2001. He has directed 30 Ph.D. dissertations and 20 M.S. theses, taught several industry short courses on reliability methods, and authored more than 300 technical publications, including two textbooks and 120 peer-reviewed journal articles.
Professor Mahadevan's professional service activities include Technical Chair and General Chair of the AIAA/ASME/ASCE/AHS/ASC Structures, Dynamics and Materials (SDM) Conferences (2005, 2010); Technical Chair and General Chair of the AIAA Non-Deterministic Approaches Conferences (2007, 2008); Chair, Executive Committee, Aerospace Division, ASCE (2004-2005); Chair, Probabilistic Methods Committee, Engineering Mechanics Institute, ASCE (2008-present); Chair, Fatigue and Fracture Reliability Committee, Structural Engineering Institute, ASCE (2001-2005); Associate Editor, Journal of Structural Engineering, ASCE (2006-present); Associate Editor, International Journal of Reliability and Safety (2005-present); and Member of Editorial Board for several journals.
Professor Mahadevan won the ASME/Boeing Outstanding Paper Award at the AIAA/ASME/ASCE/AHS/ASC Structures, Dynamics and Materials (SDM) Conference in 1992. In 2003, he received the Distinguished Probabilistic Methods Educator Award from the Society of Automotive Engineers. In 2006, he received one of Vanderbilt University's highest honors, the Joe B. Wyatt Distinguished Professor Award. In 2008, he received the Outstanding Professional Service Award from the Aerospace Division, ASCE.
For more information on Dr. Mahadevan and the Civil and Environmental Engineering department visit www.cee.vanderbilt.edu.

Views: 1465
Vanderbilt University

Talk at the NIPS Workshop on Multi-class and Multi-label Learning in Extremely Large Label Spaces

Views: 253
Manik Varma

Optimization of Energy Systems: At the Interface of Data, Modeling, and Decision-Making
The combination of data analysis, systems modeling, and computational optimization provides a powerful framework to tackle emerging challenges in energy systems. We discuss how the constantly evolving energy technology landscape as well as interdependencies between infrastructures is promoting the development of new decision-making paradigms, algorithmic techniques, and software tools to quickly assess the performance of different technologies under diverse weather and market conditions. In particular, we present new capabilities to make strategic decisions in the face of uncertainty, across multiple spatial and temporal scales, and in the presence of conflicting priorities among stakeholders. We discuss how to use these techniques to analyze the economic performance of concentrated solar power, wind power generation, and energy storage technologies. We also demonstrate how to use these capabilities to assess the impacts of coordination (or the lack thereof) between natural gas, communication, and electrical power infrastructures.
Biography: Victor M. Zavala is the Richard H. Soit Assistant Professor in the Department of Chemical and Biological Engineering at the University of WisconsinMadison. Before joining UW-Madison, he was a computational mathematician in the Mathematics and Computer Science Division at Argonne National Laboratory. He holds a B.Sc. degree from Universidad Iberoamericana and a Ph.D. degree from Carnegie Mellon University, both in chemical engineering. He is the recipient of a U.S. Department of Energy early career award and is in the editorial board of the Journal of Process Control and Mathematical Programming Computation. His research interests are in the areas of mathematical modeling of energy and agricultural systems, high-performance computing, stochastic optimization, and model predictive control.

Views: 900
APMonitor.com

Friday, November 18, 2016
CAM Notable Alumni Lecture Series
Techniques for numerical optimization have been wildly successful in an amazingly broad range of applications. In the talk, I will go into some detail about two particular applications that are both “space related”. The first application is to the design of telescopes that can achieve unprecedentedly high-contrast making it possible to directly image extra-solar planets even though their host star is billions of times brighter and has a very small angular separation from the planet. The second application is to use optimization to find new, interesting, and often exotic solutions to the n-body problem. Finding such orbits could inform us as to what type of exoplanetary systems might exist around other nearby stars. In these two applications, I will explain enough of the physics to make the optimization problem clear and then I will show some of the results we have been able to find using state-of-the-art numerical optimization algorithms.
Bio
Robert Vanderbei is a Professor in the Department of Operations Research and Financial Engineering at Princeton University. From 2005 to 2012, he was chair of the department. In addition, he holds courtesy appointments in the Departments of Mathematics, Astrophysics, Computer Science, and Mechanical and Aerospace Engineering. He is also a member of the Program in Applied and Computational Mathematics, is a founding member of the Bendheim Center for Finance, and a former Director of the Engineering and Management Systems Program.
Beyond Princeton, he is a Fellow of the American Mathematical Society (AMS), the Society for Applied and Industrial Mathematics (SIAM) and the Institute for Operations Research and the Management Sciences (INFORMS). Within INFORMS, he has served as President of the Optimization Society and the Computing Society. He also serves on the Advisory Board for the journal Mathematical Programming Computation.
He has degrees in Chemistry (B.S.), Operations Research and Statistics (M.S.), and Applied Mathematics (M.S., Ph.D.). After receiving his Ph.D. from Cornell (1981), he was an NSF postdoc at the Courant Institute for Mathematical Sciences (NYU) for one year, then a lecturer in the Mathematics Department at the University of Illinois-Urbana/Champaign for two years before joining Bell Labs in 1984. At Bell Labs he made fundamental contributions to the field of optimization and holds three patents for his inventions. In 1990, he left Bell Labs to join Princeton University where he has been since.
In addition to hundreds of research papers, he has written three books: (i) a textbook entitled Linear Programming: Foundations and Extensions now in its fourth edition and published by Springer, (ii) Sizing Up The Universe, an introductory astronomy book written jointly with J. Richard Gott and published by National Geographic, and (iii) Real and Convex Analysis, a textbook written jointly with Erhan Cinlar and published by Springer.

Views: 45
Cornell CAM Colloquium

Sparsity and compressive sensing have had a tremendous impact in science, technology, medicine, imaging, machine learning and now, in solving multiscale problems in applied partial differential equations. l1 and related optimization solvers are a key tool in this area. The special nature of this functional allows for very fast solvers: l1 actually forgives and forgets errors in Bregman iterative methods.
At the 2013 SIAM Annual Meeting, Stanley Osher of UCLA described simple, fast algorithms and new applications ranging from sparse dynamics for PDE, new regularization paths for logistic regression and support vector machine to optimal data collection and hyperspectral image processing.

Views: 2988
Society for Industrial and Applied Mathematics

MBSE Colloquium: Yiguang Hong, "Distributed optimization of continuous-time multi-agent networks"
Monday, December 5, 2016
10:00 a.m.
1146 AV Williams Building
Distributed optimization of continuous-time multi-agent networks
Yiguang Hong
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
(Roundtable at 2 pm in 1146 AVW)
Abstract
In this talk, we introduce some of our recent results on distributed convex optimization design of continuous-time multi-agent systems. After providing background and preliminaries, we start with distributed convex computation. Then we study some fundamental problems of distributed optmization with various constraints based on gradient and consensus. Moreover, we also extend our results to genearalized cases by considering uncertainties (such as approxiate gradients and external disturbance) and the agents with nonlinear or high order dynmics. In our study, we find a good connection between convex optimizaiton and nonlinear control.
Biography
Yiguang Hong received his B.S. and M.S. degrees from Peking University, China, and the Ph.D. degree from the Chinese Academy of Sciences (CAS), China. He is currently a Professor in Academy of Mathematics and Systems Science, CAS, and serves as the Director of Key Lab of Systems and Control, CAS and the Director of the Information Technology Division, National Center for Mathematics and Interdisciplinary Sciences, CAS. His current research interests include nonlinear control, multi-agent systems, distributed optimization and social networks. Prof. Hong serves as Editor-in-Chief of Control Theory and Technology and Deputy Editor-in-Chief of Acta Automatica Sinca. He also serves or served as Associate Editors for many journals including the IEEE Transactions on Automatic Control, IEEE Transactions on Control of Network Systems, IEEE Control Systems Magazine, and Nonlinear Analysis: Hybrid Systems. He is a recipient of the Guang Zhaozhi Award at the Chinese Control Conference, Young Author Prize of the IFAC World Congress, Young Scientist Award of CAS, and the Youth Award for Science and Technology of China, and the National Natural Science Prize of China. One of his papers became a Most Cited Article of Automatica during 2006-2010, with current citations over 1000 (according to google scholar).

Views: 210
ISR UMD

Many new theoretical challenges have arisen in the area of gradient-based optimization for large-scale statistical data analysis, driven by the needs of applications and the opportunities provided by new hardware and software platforms. I discuss several recent, related results in this area: (1) a new framework for understanding Nesterov acceleration, obtained by taking a continuous-time, Lagrangian/Hamiltonian/symplectic perspective, (2) a discussion of how to escape saddle points efficiently in nonconvex optimization, and (3) the acceleration of Langevin diffusion.
See more at https://www.microsoft.com/en-us/research/videos/ai-distinguished-lecture-series/

Views: 1701
Microsoft Research

Foundation for Offshore Structures by Dr. S. Nallayarasu,Department of Ocean Engineering,IIT Madras.For more details on NPTEL visit http://nptel.ac.in

Views: 2684
nptelhrd

MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015
View the complete course: https://ocw.mit.edu/RES-9-003SU15
Instructor: Surya Ganguli
Describes how the application of methods from statistical physics to the analysis of high-dimensional data can provide theoretical insights into how deep neural networks can learn to perform functions such as object categorization.
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu

Views: 849
MIT OpenCourseWare

Stochastic gradient descent is a gradient descent optimization method for minimizing an objective function that is written as a sum of differentiable functions.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video

Views: 1064
Audiopedia

EE380: Computer Systems Colloquium Seminar
"How Behavior Spreads"
Speaker: Damon Centola, University of Pennsylvania
About the talk:
New social movements, technologies, and public-health initiatives often struggle to take off, yet many diseases disperse rapidly without issue. Can the lessons learned from the viral diffusion of diseases be used to improve the spread of beneficial behaviors and innovations? In this talk, I discuss several new breakthroughs in the science of network diffusion, and how these advances have improved our understanding of how changes in societal behavior--in voting, health, technology, and finance--occur, and the ways social networks can be used to influence how they propagate. The findings show that the same conditions accelerating the viral expansion of an epidemic unexpectedly inhibit the spread of behaviors. I show how many of the most well-known, intuitive ideas about how social networks function have in fact been responsible for causing past diffusion efforts to fail. I present new findings and new network methods that have been used to enable social change efforts to succeed much more effectively.
For futher reading please consult:
Research Group Site: https://ndg.asc.upenn.edu/
Book Site: https://www.amazon.com/How-Behavior-Spreads-Contagions-Analytical/dp/0691175314
Talk Venue
For this talk, the speaker will be live on video from a remote site.
About the Speaker:
Damon Centola is an Associate Professor in the Annenberg School for Communication and the School of Engineering and Applied Sciences at the University of Pennsylvania, where he is Director of the Network Dynamics Group. Before coming to Penn, he was an Assistant Professor at M.I.T. and a Robert Wood Johnson Fellow at Harvard University.
His research includes social networks, social epidemiology, and web-based experiments on diffusion and cultural evolution. His work has been published across several disciplines in journals such as Science, Proceedings of the National Academy of Sciences, American Journal of Sociology, and Journal of Statistical Physics. Damon received the American Sociological Association's Award for Outstanding Article in Mathematical Sociology in 2006, 2009, and 2011, and was awarded the ASA's 2011 Goodman Prize for Outstanding Contributions to Sociological Methodology and the 2017 James Coleman Award for Outstanding Research in Rationality and Society. He was a developer of the NetLogo agent based modeling environment, and was awarded a U.S. Patent for inventing a method to promote diffusion in online networks. He is a member of the Sci Foo community and Fellow of the Center for Advanced Study in the Behavioral Sciences at Stanford University. He is the author of How Behavior Spreads, from Princeton University Press, and is co-editor of the Analytical Sociology series for Princeton Press.
Popular accounts of Damon's work have appeared in The New York Times, The Washington Post, The Wall Street Journal, Wired, TIME, and CNN. His research has been funded by the National Science Foundation, the Robert Wood Johnson Foundation, the National Institutes of Health, the James S. McDonnell Foundation, and the Hewlett Foundation.
For more information about this seminar and its speaker, you can visit https://ee380.stanford.edu/Abstracts/181114.html
Support for the Stanford Colloquium on Computer Systems Seminar Series provided by the Stanford Computer Forum.
Colloquium on Computer Systems Seminar Series (EE380) presents the current research in design, implementation, analysis, and use of computer systems. Topics range from integrated circuits to operating systems and programming languages. It is free and open to the public, with new lectures each week.
Learn more: http://bit.ly/WinYX5

Views: 648
stanfordonline

In machine learning, support vector machines (SVMs, also support vector networks) are supervised learning models with associated learning algorithms that analyze data and recognize patterns, used for classification and regression analysis. Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that assigns new examples into one category or the other, making it a non-probabilistic binary linear classifier. An SVM model is a representation of the examples as points in space, mapped so that the examples of the separate categories are divided by a clear gap that is as wide as possible. New examples are then mapped into that same space and predicted to belong to a category based on which side of the gap they fall on.
In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the kernel trick, implicitly mapping their inputs into high-dimensional feature spaces.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video

Views: 1184
Audiopedia

This demonstrates how to add several types of splines to Microsoft Excel with an add-in named Data Curve Fit Creator Add-in. In particular we show here the "Bessel spline" and a "One Way" (monotonic) spline. Both of these splines are similar to a cubic spline but can be better behaved (fewer unwanted wiggles and oscillations in the curve).
Download free trial and learn more at:
http://www.srs1software.com/DataCurveFitCreator.aspx

Views: 1645
SRS1Software

MATLAB and Python solutions to the Aly Chan dynamic singular problem. Dynamic optimization solution with the APMonitor Optimization Suite. Download solution from http://apmonitor.com/do/index.php/Main/MoreDynamicOptimizationBenchmarks
Aly G.M. and Chan W.C. Application of a modified quasilinearization technique to totally singular optimal problems. International Journal of Control, 17(4): 809-815, 1973.

Views: 193
APMonitor.com

The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation.
The most important application is in data fitting. The best fit in the least-squares sense minimizes the sum of squared residuals, a residual being the difference between an observed value and the fitted value provided by a model. When the problem has substantial uncertainties in the independent variable (the 'x' variable), then simple regression and least squares methods have problems; in such cases, the methodology required for fitting errors-in-variables models may be considered instead of that for least squares.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video

Views: 160
Audiopedia

UTRC CDS Invited Lecture: Javad Lavaei "Graph-Theoretic Convexification of Polynomial Optimization"
Friday, November 18, 2016
10:00 a.m.
2168 A V Williams
UTRC Control and Dynamical Systems Invited Lecture Series
Graph-Theoretic Convexification of Polynomial Optimization Problems with Applications to Power Systems and Distributed Control
Javad Lavaei
Assistant Professor
Department of Industrial Engineering and Operations Research
University of California, Berkeley
Abstract
The area of polynomial optimization has been actively studied in computer science, operations research, applied mathematics and engineering, where the goal is to find a high-quality solution using an efficient computational method. This area has attracted much attention in the control community since several long-standing control problems could be converted to polynomial optimization problems. The current researches on this area have been mostly focused on various important questions: i) how does the underlying structure of an optimization problem affect its complexity? Ii) how does sparsity help? iii) how to find a near globally optimal solution whenever it is hard to find a global minimum? iv) how to design an efficient numerical algorithm for large-scale non-convex optimization problems? v) how to deal with problems with a mix of continuous and discrete variables? In this talk, we will develop a unified mathematical framework to study the above problems. Our framework rests on recent advances in graph theory and optimization, including the notions of OS-vertex sequence and treewidth, matrix completion, semidefinite programming, and low-rank optimization. We will also apply our results to two areas of power systems and distributed control. In particular, we will discuss how our results could be used to address several hard problems for power systems such as optimal power flow (OPF), security-constrained OPF, state estimation, and unit commitment.
Biography
Javad Lavaei is an Assistant Professor in the Department of Industrial Engineering and Operations Research at University of California, Berkeley. He was an Assistant Professor in Electrical Engineering at Columbia University from 2012 to 2015. He received the Ph.D. degree in Control & Dynamical Systems from the California Institute of Technology in 2011, and was a postdoctoral scholar in Electrical Engineering and Precourt Institute for Energy at Stanford University for one year. He is the recipient of the Milton and Francis Clauser Doctoral Prize for the best university-wide Ph.D. thesis, entitled "Large-Scale Complex Systems: From Antenna Circuits to Power Grids". He researches on optimization theory, control theory and power systems. He has won several awards, including DARPA Young Faculty Award, Office of Naval Research Young Investigator Award, National Science Foundation CAREER Award, Resonate Award, Google Faculty Research Award, Governor General of Canada Academic Gold Medal, Northeastern Association of Graduate Schools Master's Thesis Award, and Silver Medal in the 1999 International Mathematical Olympiad. Javad Lavaei is an associate editor of IEEE Transactions on Smart Grid and serves on the conference editorial board of IEEE Control Systems Society and European Control Association. He was a finalist (as an advisor) for the Best Student Paper Award at the 53rd IEEE Conference on Decision and Control 2014. His journal paper entitled "Zero Duality Gap in Optimal Power Flow Problem" has received a prize paper award given by the IEEE PES Power System Analysis Computing and Economics Committee in 2015. He is a co-recipient of the 2015 INFORMS Optimization Society Prize for Young Researchers, and the recipient of the 2016 Donald P. Eckman Award given by the American Automatic Control Council.

Views: 564
ISR UMD

Kenneth M. Golden is a Distinguished Professor of Mathematics and Adjunct Professor of Bioengineering at the University of Utah. His scientific interests lie in sea ice, climate, composite materials, percolation theory, statistical physics, diffusion processes, and inverse problems. He has published papers in journals in mathematics, physics, geophysics, oceanography, ecology, remote sensing, electrical engineering, mechanical engineering, and biomechanics, and given over 400 invited lectures on six continents, including three presentations in the US Congress. Golden has journeyed seven times to Antarctica and eleven times to the Arctic to study sea ice. In 2011, he was selected as a Fellow of the Society for Industrial and Applied Mathematics for "extraordinary interdisciplinary work on the mathematics of sea ice," and in 2013 he was an Inaugural Fellow of the American Mathematical Society. Professor Golden received the University of Utah's highest award for teaching in 2007 and for research in 2012.
In 2014, Golden was elected as a Fellow of the Explorers Club, whose members have included Robert Peary, Sir Edmund Hillary, Neil Armstrong, and Jane Goodall. His polar expeditions and mathematical work have been covered in over 50 newspaper, magazine, and web articles, including profiles in Science, Science News, Scientific American and Physics Today. He has also been interviewed numerous times on radio and television, and featured in videos produced by the National Science Foundation and NBC News.
Brown University
April 26, 2017

Views: 490
Brown University

[email protected] is proud to present Nassim N. Taleb, author of
Fooled By Randomness and The Black Swan, talking about his new book.

Views: 172493
Talks at Google

http://smartech.gatech.edu/jspui/handle/1853/34551
Title: Composite Objective Optimization and Learning for Massive Datasets
Author: Singer, Yoram
Affiliation: Google Research
Georgia Institute of Technology. School of Computational Science and Engineering
Slides: http://www.cs.berkeley.edu/~jduchi/projects/DuchiSi10_mmds.pdf
Keywords: Machine learning, AdaGrad, Datasets
Issue Date: 3-Sep-2010
Publisher: Georgia Institute of Technology
Abstract: Composite objective optimization is concerned with the problem of minimizing a two-term objective function which consists of an empirical loss function and a regularization function. Application with massive datasets often employ a regularization term which is non-differentiable or structured, such as L1 or mixed-norm regularization. Such regularizers promote sparse solutions and special structure of the parameters of the problem, which is a desirable goal for datasets of extremely high-dimensions. In this talk, we discuss several recently developed methods for performing composite objective minimization in the online learning and stochastic optimization settings. We start with a description of extensions of the well-known forward-backward splitting method to stochastic objectives. We then generalize this paradigm to the family of mirrordescent algorithms. Our work builds on recent work which connects proximal minimization to online and stochastic optimization. We focus in the algorithmic part on a new approach, called AdaGrad, in which the proximal function is adapted throughout the course of the algorithm in a data-dependent manner. This temporal adaptation metaphorically allows us to find needles in haystacks as the algorithm is able to single out very predictive yet rarely observed features. We conclude with several experiments on large-scale datasets that demonstrate the merits of composite objective optimization and underscore superior performance of various instantiations of AdaGrad.
Description: Yoram Singer, Senior Research Scientist of Google Research presented a lecture on September 3, 2010 at 2:00 pm in room 1447 of the Klaus Advanced Computing Building on the Georgia Tech campus.
Yoram Singer is a senior research scientist at Google. From 1999 through 2007 he was an associate professor at the Hebrew University of Jerusalem, Israel. He was member of the technical staff at AT&T Research from 1995 through 1999. He served as an associate editor of Machine Learning Journal and is now on the editorial board of the Journal of Machine Learning Research and IEEE Signal Processing Magazine. He was the co-chair of COLT'04 and NIPS'07. He is a AAAI Fellow and won for several awards for his research papers, most recently the 10 years retrospect award for the most influential paper of ICML 2000.
Runtime: 56:18 minutes

Views: 1462
npresearch

Abstract:
The last decade has witnessed burgeoning developments in the reconstruction of signals based on exploiting their low-dimensional structures, particularly their sparsity, block-sparsity, and low-rankness. The reconstruction performance of these signals is heavily dependent on the structure of the operating matrix used in sensing. The quality of these matrices in the context of signal recovery is usually quantified by the restricted isometry constant and its variants. However, the restricted isometry constant and its variants are extremely difficult to compute.
We present a framework for analytically computing the performance of the recovery of signals with sparsity structures. We define a family of incoherence measures to quantify the goodness of arbitrary sensing matrices. Our primary contribution is the design of efficient algorithms, based on linear programming and second order cone programming, to compute these incoherence measures. As a by-product, we implement efficient algorithms to verify sufficient conditions for exact signal recovery in the noise-free case. The utility of the proposed incoherence measures lies in their relationship to the performance of reconstruction methods. We derive closed-form expressions of bounds on the recovery errors of convex relaxation algorithms in terms of these measures.
Bio:
Arye Nehorai is the Eugene and Martha Lohman Professor and Chair of the Preston M. Green Department of Electrical and Systems Engineering, Professor in the Department of Biomedical Engineering and in the Division of Biology and Biomedical Studies at Washington University in St. Louis. Under his leadership as department chair, the undergraduate enrollment has more than tripled in the last four years. He received the B.Sc. and M.Sc. degrees from the Technion, Israel and the Ph.D. from Stanford University, California.
Dr. Nehorai had served as Editor-in-Chief of the IEEE Transactions on Signal Processing from 2000 to 2002. From 2003 to 2005 he was the Vice President (Publications) of the IEEE Signal Processing Society (SPS), the Chair of the Publications Board, and a member of the Executive Committee of this Society.
Dr. Nehorai received the 2006 IEEE SPS Technical Achievement Award and the 2010 IEEE SPS Meritorious Service Award. He was elected Distinguished Lecturer of the IEEE SPS for a term lasting from 2004 to 2005. He received several best paper awards in IEEE journals and conferences. He is a Fellow of the IEEE, the Royal Statistical Society, and the AAAS.

Views: 104
NC State ECE

Foundations of Optimization by Dr. Joydeep Dutta,Department of Mathematics,IIT Kanpur.For more details on NPTEL visit http://nptel.ac.in

Views: 2081
nptelhrd

UPDATE: The workshop proceedings will be published in a special issue of The Journal Of Machine Learning Research prior to the workshop date. For that reason, submissions are extended to 10 pages (excluding references and appendix) in JMLR format. The authors of accepted submissions will be asked to provide a camera-ready version within 7 days of acceptance notification. lt br gt lt br gt lt br gt The problem of extracting features from given data is of critical importance for the successful application of machine learning. Feature extraction, as usually understood, seeks for an optimal transformation from raw data into features that can be used as an input for a learning algorithm. In recent times this problem has been attacked using a growing number of diverse techniques that originated in separate research communities: from PCA and LDA to manifold and metric learning. It is the goal of this workshop to provide a platform to exchange ideas and compare results across these techniques. lt br gt lt br gt The workshop will consist of three sessions, each dedicated to a specific open problem in the area of feature extraction. The sessions will start with invited talks and conclude with panel discussions, where the audience will engage into debates with speakers and organizers. lt br gt lt br gt We welcome submissions from sub-areas such as general embedding techniques, metric learning, scalable nonlinear features, deep neural networks. lt br gt lt br gt More often than not, studies in each of these areas do not compare or evaluate methods found in the other areas. It is the goal of this workshop to begin the discussions needed to remedy this. We encourage submissions to foster open discussions around such important questions, which include, but are not limited to: lt br gt lt br gt 1. Scalability. We have recently managed to scale up convex methods. Most remarkably, approximating kernel functions via random Fourier features have enabled kernel machines to match the DNNs. That inspired many efficient feature extraction methods, for instance Monte Carlo methods improved the results of Fourier features as well as approximating polynomial kernels via explicit feature maps showed remarkable performance. What does it all means for the prospects of convex scalable methods? Can they become state of the art in the nearest future? lt br gt lt br gt 2. Convex and non-convex feature extraction. While deep nets suffer from non-convexity and the lack of theoretical guarantees, kernel machines are convex and well studied mathematically. Thus, it is extremely tempting for us to resort to kernels in understanding neural nets. Can we shed more light on their connection? lt br gt lt br gt 3. Balance between extraction and classification stages. We often see in real world applications (e.g. spam detection, audio filtering) that feature extraction is CPU-heavy compared to classification. The classic way to balance them was to sparsify the choice of features with L-1 regularization. A promising alternative is to use trees of classifiers. However, this problem is NP hard, so a number of relaxations has been suggested. Which relaxations are better and will the tree-based approaches to extraction/classification tradeoff become the state of the art? lt br gt lt br gt 4. Supervised vs. Unsupervised. Can we understand, which methods are most useful for particular settings and why? lt br gt lt br gt 5. Theory vs. Practice: Certain methods are supported by significant theoretical guarantees, but how do these guarantees translate into performance in practice?

Views: 244
NIPS

Advanced Process Control by Prof.Sachin C.Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

Views: 2396
nptelhrd

Geotechnical Earthquake Engineering by Dr. Deepankar Choudhury,Department of Civil Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

Views: 915
nptelhrd

Speaker: Dr. Somayeh Sojoudi, Assistant Professor, EE & CS Department, UC Berkley
Learning Large-Scale Sparse Graphical Models: Theory, Algorithm, and Applications
The Engineering Lecture Series has been designed to benefit the Sonoma State student and faculty in the School of Science and Technology, high tech and biotech industries and related businesses and community in the North Bay Region.
The Lecture Series will cover a broad range of topics with focus on recent developments and trends and will provide a platform for interaction and exchange of ideas among the audience.
Attendance is open to the students, faculty and staff of SSU and other academic institutions, engineers and scientists from the industries, members of the Business Community and members of the Community, in general. A parking permit is required to park on campus and is available for $5.00 at machines in the parking lots. Talks are otherwise free.

Views: 583
CSUSonoma

UPDATE: The workshop proceedings will be published in a special issue of The Journal Of Machine Learning Research prior to the workshop date. For that reason, submissions are extended to 10 pages (excluding references and appendix) in JMLR format. The authors of accepted submissions will be asked to provide a camera-ready version within 7 days of acceptance notification. lt br gt lt br gt lt br gt The problem of extracting features from given data is of critical importance for the successful application of machine learning. Feature extraction, as usually understood, seeks for an optimal transformation from raw data into features that can be used as an input for a learning algorithm. In recent times this problem has been attacked using a growing number of diverse techniques that originated in separate research communities: from PCA and LDA to manifold and metric learning. It is the goal of this workshop to provide a platform to exchange ideas and compare results across these techniques. lt br gt lt br gt The workshop will consist of three sessions, each dedicated to a specific open problem in the area of feature extraction. The sessions will start with invited talks and conclude with panel discussions, where the audience will engage into debates with speakers and organizers. lt br gt lt br gt We welcome submissions from sub-areas such as general embedding techniques, metric learning, scalable nonlinear features, deep neural networks. lt br gt lt br gt More often than not, studies in each of these areas do not compare or evaluate methods found in the other areas. It is the goal of this workshop to begin the discussions needed to remedy this. We encourage submissions to foster open discussions around such important questions, which include, but are not limited to: lt br gt lt br gt 1. Scalability. We have recently managed to scale up convex methods. Most remarkably, approximating kernel functions via random Fourier features have enabled kernel machines to match the DNNs. That inspired many efficient feature extraction methods, for instance Monte Carlo methods improved the results of Fourier features as well as approximating polynomial kernels via explicit feature maps showed remarkable performance. What does it all means for the prospects of convex scalable methods? Can they become state of the art in the nearest future? lt br gt lt br gt 2. Convex and non-convex feature extraction. While deep nets suffer from non-convexity and the lack of theoretical guarantees, kernel machines are convex and well studied mathematically. Thus, it is extremely tempting for us to resort to kernels in understanding neural nets. Can we shed more light on their connection? lt br gt lt br gt 3. Balance between extraction and classification stages. We often see in real world applications (e.g. spam detection, audio filtering) that feature extraction is CPU-heavy compared to classification. The classic way to balance them was to sparsify the choice of features with L-1 regularization. A promising alternative is to use trees of classifiers. However, this problem is NP hard, so a number of relaxations has been suggested. Which relaxations are better and will the tree-based approaches to extraction/classification tradeoff become the state of the art? lt br gt lt br gt 4. Supervised vs. Unsupervised. Can we understand, which methods are most useful for particular settings and why? lt br gt lt br gt 5. Theory vs. Practice: Certain methods are supported by significant theoretical guarantees, but how do these guarantees translate into performance in practice?

Views: 89
NIPS

Advanced Networks Colloquium: Yiguang Hong, "Social opinion dynamics--Agreement or disagreement"
Friday, December 9, 2016
11:00 a.m.
1146 AV Williams Building; Roundtable Thursday Dec. 8, 2 pm, Room 2120 AV Williams (UMIACS conference room)
Yiguang Hong
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Roundtable Thursday Dec. 8, 2 pm, Room 2120 AV Williams (UMIACS conference room)
Abstract
The talk mainly focuses on the recent achievement about analysis and "control" of bounded confidence opinion dynamics. We introduce some well-known bounded-confidence opinion models of social networks (such as the Hegselmann-Krause model and Deffuant-Weisbuch model), and the related technical challenges. Note that the models are highly nonlinear and whose interaction topologies are time-varying and state-dependent. Therefore, the analysis for such models are usually much more difficult than that for the opinion models described by state-independent graphs. We first demonstrate two basic disagreement phenomena: fragmentation and fluctuation, and give strict mathematical analysis for opinion disagreement resulting from some opinion exchange rules. Then we discuss the "control" of opinion dynamics, called opinion intervention, in order to alter opinion evolution in social networks, and theoretically prove that simple noise-injection strategies are effective to enhance the opinion agreement.
Biography
Yiguang Hong received his B.S. and M.S. degrees from Peking University, China, and the Ph.D. degree from the Chinese Academy of Sciences (CAS), China. He is currently a Professor in Academy of Mathematics and Systems Science, CAS, and serves as the Director of Key Lab of Systems and Control, CAS and the Director of the Information Technology Division, National Center for Mathematics and Interdisciplinary Sciences, CAS. His current research interests include nonlinear control, multi-agent systems, distributed optimization and social networks. Prof. Hong serves as Editor-in-Chief of Control Theory and Technology and Deputy Editor-in-Chief of Acta Automatica Sinca. He also serves or served as Associate Editors for many journals including the IEEE Transactions on Automatic Control, IEEE Transactions on Control of Network Systems, IEEE Control Systems Magazine, and Nonlinear Analysis: Hybrid Systems. He is a recipient of the Guang Zhaozhi Award at the Chinese Control Conference, Young Author Prize of the IFAC World Congress, Young Scientist Award of CAS, and the Youth Award for Science and Technology of China, and the National Natural Science Prize of China. One of his papers became a Most Cited Article of Automatica during 2006-2010, with current citations over 1000 (according to google scholar).

Views: 114
ISR UMD

UPDATE: The workshop proceedings will be published in a special issue of The Journal Of Machine Learning Research prior to the workshop date. For that reason, submissions are extended to 10 pages (excluding references and appendix) in JMLR format. The authors of accepted submissions will be asked to provide a camera-ready version within 7 days of acceptance notification. lt br gt lt br gt lt br gt The problem of extracting features from given data is of critical importance for the successful application of machine learning. Feature extraction, as usually understood, seeks for an optimal transformation from raw data into features that can be used as an input for a learning algorithm. In recent times this problem has been attacked using a growing number of diverse techniques that originated in separate research communities: from PCA and LDA to manifold and metric learning. It is the goal of this workshop to provide a platform to exchange ideas and compare results across these techniques. lt br gt lt br gt The workshop will consist of three sessions, each dedicated to a specific open problem in the area of feature extraction. The sessions will start with invited talks and conclude with panel discussions, where the audience will engage into debates with speakers and organizers. lt br gt lt br gt We welcome submissions from sub-areas such as general embedding techniques, metric learning, scalable nonlinear features, deep neural networks. lt br gt lt br gt More often than not, studies in each of these areas do not compare or evaluate methods found in the other areas. It is the goal of this workshop to begin the discussions needed to remedy this. We encourage submissions to foster open discussions around such important questions, which include, but are not limited to: lt br gt lt br gt 1. Scalability. We have recently managed to scale up convex methods. Most remarkably, approximating kernel functions via random Fourier features have enabled kernel machines to match the DNNs. That inspired many efficient feature extraction methods, for instance Monte Carlo methods improved the results of Fourier features as well as approximating polynomial kernels via explicit feature maps showed remarkable performance. What does it all means for the prospects of convex scalable methods? Can they become state of the art in the nearest future? lt br gt lt br gt 2. Convex and non-convex feature extraction. While deep nets suffer from non-convexity and the lack of theoretical guarantees, kernel machines are convex and well studied mathematically. Thus, it is extremely tempting for us to resort to kernels in understanding neural nets. Can we shed more light on their connection? lt br gt lt br gt 3. Balance between extraction and classification stages. We often see in real world applications (e.g. spam detection, audio filtering) that feature extraction is CPU-heavy compared to classification. The classic way to balance them was to sparsify the choice of features with L-1 regularization. A promising alternative is to use trees of classifiers. However, this problem is NP hard, so a number of relaxations has been suggested. Which relaxations are better and will the tree-based approaches to extraction/classification tradeoff become the state of the art? lt br gt lt br gt 4. Supervised vs. Unsupervised. Can we understand, which methods are most useful for particular settings and why? lt br gt lt br gt 5. Theory vs. Practice: Certain methods are supported by significant theoretical guarantees, but how do these guarantees translate into performance in practice?

Views: 153
NIPS

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Mathematical_optimization
00:01:02 1 Optimization problems
00:08:17 2 Notation
00:08:33 2.1 Minimum and maximum value of a function
00:10:33 2.2 Optimal input arguments
00:17:31 3 History
00:18:38 4 Major subfields
00:24:43 4.1 Multi-objective optimization
00:26:48 4.2 Multi-modal optimization
00:27:53 5 Classification of critical points and extrema
00:28:05 5.1 Feasibility problem
00:29:01 5.2 Existence
00:29:34 5.3 Necessary conditions for optimality
00:30:43 5.4 Sufficient conditions for optimality
00:31:52 5.5 Sensitivity and continuity of optima
00:32:30 5.6 Calculus of optimization
00:34:02 6 Computational optimization techniques
00:34:35 6.1 Optimization algorithms
00:38:54 6.2 Iterative methods
00:44:03 6.3 Global convergence
00:45:08 6.4 Heuristics
00:45:39 7 Applications
00:45:49 7.1 Mechanics
00:47:20 7.2 Economics and finance
00:49:52 7.3 Electrical engineering
00:50:43 7.4 Civil engineering
00:51:12 7.5 Operations research
00:51:54 7.6 Control engineering
00:52:39 7.7 Geophysics
00:53:09 7.8 Molecular modeling
00:53:26 7.9 Computational systems biology
00:54:22 8 Solvers
00:54:31 9 See also
00:54:41 10 Notes
00:54:50 11 Further reading
00:54:59 11.1 Comprehensive
00:55:08 11.1.1 Undergraduate level
00:57:05 11.1.2 Graduate level
01:02:10 11.2 Continuous optimization
01:06:20 11.3 Combinatorial optimization
01:09:34 11.4 Relaxation (extension method)
01:11:28 12 Journals
01:12:06 13 External links
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.7803214045269206
Voice name: en-US-Wavenet-D
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain (or input), including a variety of different types of objective functions and different types of domains.

Views: 2
wikipedia tts

Optimal Control, Guidance and Estimation by Dr. Radhakant Padhi, Department of Aerospace Engineering, IISc Bangalore. For more details on NPTEL visit http://nptel.iitm.ac.in

Views: 764
nptelhrd

This is an audio version of the Wikipedia Article:
Mathematical economics
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
You can find other Wikipedia audio articles too at:
https://www.youtube.com/channel/UCuKfABj2eGyjH3ntPxp4YeQ
You can upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
"The only true wisdom is in knowing you know nothing."
- Socrates
SUMMARY
=======
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. By convention, these applied methods are beyond simple geometry, such as differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, and other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.Mathematics allows economists to form meaningful, testable propositions about wide-ranging and complex subjects which could less easily be expressed informally. Further, the language of mathematics allows economists to make specific, positive claims about controversial or contentious subjects that would be impossible without mathematics. Much of economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify assumptions and implications.Broad applications include:
optimization problems as to goal equilibrium, whether of a household, business firm, or policy maker
static (or equilibrium) analysis in which the economic unit (such as a household) or economic system (such as a market or the economy) is modeled as not changing
comparative statics as to a change from one equilibrium to another induced by a change in one or more factors
dynamic analysis, tracing changes in an economic system over time, for example from economic growth.Formal economic modeling began in the 19th century with the use of differential calculus to represent and explain economic behavior, such as utility maximization, an early economic application of mathematical optimization. Economics became more mathematical as a discipline throughout the first half of the 20th century, but introduction of new and generalized techniques in the period around the Second World War, as in game theory, would greatly broaden the use of mathematical formulations in economics.This rapid systematizing of economics alarmed critics of the discipline as well as some noted economists. John Maynard Keynes, Robert Heilbroner, Friedrich Hayek and others have criticized the broad use of mathematical models for human behavior, arguing that some human choices are irreducible to mathematics.

Views: 13
wikipedia tts

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Mathematical_optimization
00:01:01 1 Optimization problems
00:07:58 2 Notation
00:08:15 2.1 Minimum and maximum value of a function
00:10:10 2.2 Optimal input arguments
00:16:54 3 History
00:18:00 4 Major subfields
00:23:56 4.1 Multi-objective optimization
00:25:59 4.2 Multi-modal optimization
00:27:03 5 Classification of critical points and extrema
00:27:15 5.1 Feasibility problem
00:28:10 5.2 Existence
00:28:42 5.3 Necessary conditions for optimality
00:29:49 5.4 Sufficient conditions for optimality
00:30:58 5.5 Sensitivity and continuity of optima
00:31:35 5.6 Calculus of optimization
00:33:06 6 Computational optimization techniques
00:33:39 6.1 Optimization algorithms
00:37:51 6.2 Iterative methods
00:42:51 6.3 Global convergence
00:43:56 6.4 Heuristics
00:44:27 7 Applications
00:44:37 7.1 Mechanics
00:46:06 7.2 Economics and finance
00:48:33 7.3 Electrical engineering
00:49:22 7.4 Civil engineering
00:49:52 7.5 Operations research
00:50:32 7.6 Control engineering
00:51:17 7.7 Geophysics
00:51:46 7.8 Molecular modeling
00:52:02 7.9 Computational systems biology
00:52:56 8 Solvers
00:53:06 9 See also
00:53:15 10 Notes
00:53:24 11 Further reading
00:53:34 11.1 Comprehensive
00:53:43 11.1.1 Undergraduate level
00:55:31 11.1.2 Graduate level
01:00:12 11.2 Continuous optimization
01:03:58 11.3 Combinatorial optimization
01:06:52 11.4 Relaxation (extension method)
01:08:41 12 Journals
01:09:18 13 External links
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.8537923532584719
Voice name: en-GB-Wavenet-D
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain (or input), including a variety of different types of objective functions and different types of domains.

Views: 2
wikipedia tts

This is an audio version of the Wikipedia Article:
Statistics
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
You can find other Wikipedia audio articles too at:
https://www.youtube.com/channel/UCuKfABj2eGyjH3ntPxp4YeQ
You can upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
"The only true wisdom is in knowing you know nothing."
- Socrates
SUMMARY
=======
Statistics is a branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation. In applying statistics to, for example, a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.
See glossary of probability and statistics.
When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.
Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.
A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a "false positive") and Type II errors (null hypothesis fails to be rejected and an actual difference between populations is missed giving a "false negative"). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.
Statistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more heavily from calculus and probability theory. In more recent years statistics has relied more on statistical software to produce tests such as descriptive analysis.

Views: 6
wikipedia tts

Model predictive control is an advanced method of process control that has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification. The main advantage of MPC is the fact that it allows the current timeslot to be optimized, while keeping future timeslots in account. This is achieved by optimizing a finite time-horizon, but only implementing the current timeslot. MPC has the ability to anticipate future events and can take control actions accordingly. PID and LQR controllers do not have this predictive ability. MPC is nearly universally implemented as a digital control, although there is research into achieving faster response times with specially designed analog circuitry.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video

Views: 570
Audiopedia

In mathematics, a Lie group is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Sophus Lie, who laid the foundations of the theory of continuous transformation groups. The term groupes de Lie first appeared in French in 1893 in the thesis of Lie’s student Arthur Tresse, page 3.
Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. They provide a natural framework for analysing the continuous symmetries of differential equations, in much the same way as permutation groups are used in Galois theory for analysing the discrete symmetries of algebraic equations. An extension of Galois theory to the case of continuous symmetry groups was one of Lie's principal motivations.
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Audiopedia

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Outline_of_science
00:01:04 1 Essence of science
00:02:18 2 Scientific method
00:07:04 3 Branches of science
00:07:28 3.1 Natural science
00:08:35 3.2 Formal science
00:55:27 3.3 Social science
00:56:37 3.4 Applied science
00:57:07 4 How scientific fields differ
00:58:13 5 Politics of science
00:59:33 6 History of science
01:01:46 6.1 By period
01:04:08 6.1.1 By date
01:05:03 6.2 By field
01:08:58 6.3 By region
01:09:07 6.3.1 History of science in present states, by continent
01:09:25 6.3.2 History of science in historic states
01:09:59 7 Philosophy of science
01:10:20 8 Scientific community
01:10:47 8.1 Scientific organizations
01:11:07 8.2 Scientists
01:11:50 8.2.1 Types of scientist
01:11:59 8.2.1.1 By field
01:28:07 8.2.1.2 By employment status
01:28:56 8.2.2 Famous scientists
01:33:12 9 Science education
01:33:59 10 See also
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"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
The following outline is provided as a topical overview of science:
Science – the systematic effort of acquiring knowledge—through observation and experimentation coupled with logic and reasoning to find out what can be proved or not proved—and the knowledge thus acquired. The word "science" comes from the Latin word "scientia" meaning knowledge. A practitioner of science is called a "scientist". Modern science respects objective logical reasoning, and follows a set of core procedures or rules in order to determine the nature and underlying natural laws of the universe and everything in it. Some scientists do not know of the rules themselves, but follow them through research policies. These procedures are known as the scientific method.

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wikipedia tts

This is an audio version of the Wikipedia Article:
Expected utility hypothesis
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
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"The only true wisdom is in knowing you know nothing."
- Socrates
SUMMARY
=======
In economics, game theory, and decision theory the expected utility hypothesis, concerning people's preferences with regard to choices that have uncertain outcomes (gambles), states that the subjective value associated with an individual's gamble is the statistical expectation of that individual's valuations of the outcomes of that gamble, where these valuations may differ from the dollar value of those outcomes.
Initiated by Daniel Bernoulli in 1738, this hypothesis has proven useful to explain some popular choices that seem to contradict the expected value criterion (which takes into account only the sizes of the payouts and the probabilities of occurrence), such as occur in the contexts of gambling and insurance. Until the mid-twentieth century, the standard term for the expected utility was the moral expectation, contrasted with "mathematical expectation" for the expected value.The von Neumann–Morgenstern utility theorem provides necessary and sufficient conditions under which the expected utility hypothesis holds. From relatively early on, it was accepted that some of these conditions would be violated by real decision-makers in practice but that the conditions could be interpreted nonetheless as 'axioms' of rational choice.

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wikipedia tts

This is an audio version of the Wikipedia Article:
Liu Gang
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"The only true wisdom is in knowing you know nothing."
- Socrates
SUMMARY
=======
Liu Gang (born 30 January 1961) is a Chinese scientist and revolutionary who founded the Beijing Students' Autonomous Federation. He was a prominent student leader at the Tiananmen Square protests of 1989. Liu holds a M.A. in physics from Peking University and a M.A. in computer science from Columbia University. After his exile to the United States in 1996, Liu studied technology and physics at Bell Labs in New Jersey. Liu was employed at Morgan Stanley as a Wall Street IT analyst.

Views: 1
wikipedia tts

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Outline_of_science
00:00:47 1 Essence of science
00:01:43 2 Scientific method
00:05:13 3 Branches of science
00:05:32 3.1 Natural science
00:06:22 3.2 Formal science
00:40:51 3.3 Social science
00:41:44 3.4 Applied science
00:42:08 4 How scientific fields differ
00:42:58 5 Politics of science
00:43:59 6 History of science
00:45:37 6.1 By period
00:47:24 6.1.1 By date
00:48:06 6.2 By field
00:50:59 6.3 By region
00:51:07 6.3.1 History of science in present states, by continent
00:51:22 6.3.2 History of science in historic states
00:51:48 7 Philosophy of science
00:52:05 8 Scientific community
00:52:27 8.1 Scientific organizations
00:52:44 8.2 Scientists
00:53:17 8.2.1 Types of scientist
00:53:25 8.2.1.1 By field
01:05:11 8.2.1.2 By employment status
01:05:48 8.2.2 Famous scientists
01:08:58 9 Science education
01:09:34 10 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
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Other Wikipedia audio articles at:
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Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
"There is only one good, knowledge, and one evil, ignorance."
- Socrates
SUMMARY
=======
The following outline is provided as a topical overview of science:
Science – the systematic effort of acquiring knowledge—through observation and experimentation coupled with logic and reasoning to find out what can be proved or not proved—and the knowledge thus acquired. The word "science" comes from the Latin word "scientia" meaning knowledge. A practitioner of science is called a "scientist". Modern science respects objective logical reasoning, and follows a set of core procedures or rules in order to determine the nature and underlying natural laws of the universe and everything in it. Some scientists do not know of the rules themselves, but follow them through research policies. These procedures are known as the scientific method.

Views: 3
wikipedia tts

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ranjith kumar