Large Scale Convex Optimization

Author : Ernest K. Ryu,Wotao Yin
Publisher : Cambridge University Press
Page : 320 pages
File Size : 43,9 Mb
Release : 2022-12-01
Category : Mathematics
ISBN : 9781009191067

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Large-Scale Convex Optimization by Ernest K. Ryu,Wotao Yin Pdf

Starting from where a first course in convex optimization leaves off, this text presents a unified analysis of first-order optimization methods – including parallel-distributed algorithms – through the abstraction of monotone operators. With the increased computational power and availability of big data over the past decade, applied disciplines have demanded that larger and larger optimization problems be solved. This text covers the first-order convex optimization methods that are uniquely effective at solving these large-scale optimization problems. Readers will have the opportunity to construct and analyze many well-known classical and modern algorithms using monotone operators, and walk away with a solid understanding of the diverse optimization algorithms. Graduate students and researchers in mathematical optimization, operations research, electrical engineering, statistics, and computer science will appreciate this concise introduction to the theory of convex optimization algorithms.

Author : Pontus Giselsson,Anders Rantzer
Publisher : Springer
Page : 412 pages
File Size : 53,6 Mb
Release : 2018-11-11
Category : Mathematics
ISBN : 9783319974781

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Large-Scale and Distributed Optimization by Pontus Giselsson,Anders Rantzer Pdf

This book presents tools and methods for large-scale and distributed optimization. Since many methods in "Big Data" fields rely on solving large-scale optimization problems, often in distributed fashion, this topic has over the last decade emerged to become very important. As well as specific coverage of this active research field, the book serves as a powerful source of information for practitioners as well as theoreticians. Large-Scale and Distributed Optimization is a unique combination of contributions from leading experts in the field, who were speakers at the LCCC Focus Period on Large-Scale and Distributed Optimization, held in Lund, 14th–16th June 2017. A source of information and innovative ideas for current and future research, this book will appeal to researchers, academics, and students who are interested in large-scale optimization.

Author : Vladimir Tsurkov
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 50,5 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9781475732436

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Large-scale Optimization by Vladimir Tsurkov Pdf

Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms. Audience: This book is addressed to specialists in operations research, optimization, and optimal control.

Author : Jesús M. Velásquez-Bermúdez,Marzieh Khakifirooz,Mahdi Fathi
Publisher : Springer Nature
Page : 282 pages
File Size : 50,9 Mb
Release : 2019-09-06
Category : Mathematics
ISBN : 9783030227883

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Large Scale Optimization in Supply Chains and Smart Manufacturing by Jesús M. Velásquez-Bermúdez,Marzieh Khakifirooz,Mahdi Fathi Pdf

In this book, theory of large scale optimization is introduced with case studies of real-world problems and applications of structured mathematical modeling. The large scale optimization methods are represented by various theories such as Benders’ decomposition, logic-based Benders’ decomposition, Lagrangian relaxation, Dantzig –Wolfe decomposition, multi-tree decomposition, Van Roy’ cross decomposition and parallel decomposition for mathematical programs such as mixed integer nonlinear programming and stochastic programming. Case studies of large scale optimization in supply chain management, smart manufacturing, and Industry 4.0 are investigated with efficient implementation for real-time solutions. The features of case studies cover a wide range of fields including the Internet of things, advanced transportation systems, energy management, supply chain networks, service systems, operations management, risk management, and financial and sales management. Instructors, graduate students, researchers, and practitioners, would benefit from this book finding the applicability of large scale optimization in asynchronous parallel optimization, real-time distributed network, and optimizing the knowledge-based expert system for convex and non-convex problems.

Author : Dimitri Bertsekas
Publisher : Athena Scientific
Page : 576 pages
File Size : 49,6 Mb
Release : 2015-02-01
Category : Mathematics
ISBN : 9781886529281

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Convex Optimization Algorithms by Dimitri Bertsekas Pdf

This book provides a comprehensive and accessible presentation of algorithms for solving convex optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. This is facilitated by the extensive use of analytical and algorithmic concepts of duality, which by nature lend themselves to geometrical interpretation. The book places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning. The book is aimed at students, researchers, and practitioners, roughly at the first year graduate level. It is similar in style to the author's 2009"Convex Optimization Theory" book, but can be read independently. The latter book focuses on convexity theory and optimization duality, while the present book focuses on algorithmic issues. The two books share notation, and together cover the entire finite-dimensional convex optimization methodology. To facilitate readability, the statements of definitions and results of the "theory book" are reproduced without proofs in Appendix B.

Author : Stephen P. Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 744 pages
File Size : 43,6 Mb
Release : 2004-03-08
Category : Business & Economics
ISBN : 0521833787

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Convex Optimization by Stephen P. Boyd,Lieven Vandenberghe Pdf

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Author : Thomas Frederick Coleman,Yuying Li
Publisher : SIAM
Page : 278 pages
File Size : 53,6 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 0898712688

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Large-scale Numerical Optimization by Thomas Frederick Coleman,Yuying Li Pdf

Papers from a workshop held at Cornell University, Oct. 1989, and sponsored by Cornell's Mathematical Sciences Institute. Annotation copyright Book News, Inc. Portland, Or.

Author : Heinz H. Bauschke,Patrick L. Combettes
Publisher : Springer
Page : 624 pages
File Size : 54,5 Mb
Release : 2017-02-28
Category : Mathematics
ISBN : 9783319483115

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Convex Analysis and Monotone Operator Theory in Hilbert Spaces by Heinz H. Bauschke,Patrick L. Combettes Pdf

This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.

Author : Dimitri Bertsekas
Publisher : Athena Scientific
Page : 256 pages
File Size : 43,8 Mb
Release : 2009-06-01
Category : Mathematics
ISBN : 9781886529311

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Convex Optimization Theory by Dimitri Bertsekas Pdf

An insightful, concise, and rigorous treatment of the basic theory of convex sets and functions in finite dimensions, and the analytical/geometrical foundations of convex optimization and duality theory. Convexity theory is first developed in a simple accessible manner, using easily visualized proofs. Then the focus shifts to a transparent geometrical line of analysis to develop the fundamental duality between descriptions of convex functions in terms of points, and in terms of hyperplanes. Finally, convexity theory and abstract duality are applied to problems of constrained optimization, Fenchel and conic duality, and game theory to develop the sharpest possible duality results within a highly visual geometric framework. This on-line version of the book, includes an extensive set of theoretical problems with detailed high-quality solutions, which significantly extend the range and value of the book. The book may be used as a text for a theoretical convex optimization course; the author has taught several variants of such a course at MIT and elsewhere over the last ten years. It may also be used as a supplementary source for nonlinear programming classes, and as a theoretical foundation for classes focused on convex optimization models (rather than theory). It is an excellent supplement to several of our books: Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 2017), Network Optimization(Athena Scientific, 1998), Introduction to Linear Optimization (Athena Scientific, 1997), and Network Flows and Monotropic Optimization (Athena Scientific, 1998).

Author : David A. Wismer
Publisher : McGraw-Hill Companies
Page : 358 pages
File Size : 46,7 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015047422830

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Optimization Methods for Large-scale Systems ... with Applications by David A. Wismer Pdf

Author : Gianni Pillo,Massimo Roma
Publisher : Springer
Page : 0 pages
File Size : 42,6 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 1441940146

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Large-Scale Nonlinear Optimization by Gianni Pillo,Massimo Roma Pdf

This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.

Author : Jean-Baptiste Hiriart-Urruty,Claude Lemaréchal
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642564680

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Fundamentals of Convex Analysis by Jean-Baptiste Hiriart-Urruty,Claude Lemaréchal Pdf

This book is an abridged version of the two volumes "Convex Analysis and Minimization Algorithms I and II" (Grundlehren der mathematischen Wissenschaften Vol. 305 and 306). It presents an introduction to the basic concepts in convex analysis and a study of convex minimization problems (with an emphasis on numerical algorithms). The "backbone" of bot volumes was extracted, some material deleted which was deemed too advanced for an introduction, or too closely attached to numerical algorithms. Some exercises were included and finally the index has been considerably enriched, making it an excellent choice for the purpose of learning and teaching.

Author : William W. Hager,D.W. Hearn,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 50,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461336327

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Large Scale Optimization by William W. Hager,D.W. Hearn,Panos M. Pardalos Pdf

On February 15-17, 1993, a conference on Large Scale Optimization, hosted by the Center for Applied Optimization, was held at the University of Florida. The con ference was supported by the National Science Foundation, the U. S. Army Research Office, and the University of Florida, with endorsements from SIAM, MPS, ORSA and IMACS. Forty one invited speakers presented papers on mathematical program ming and optimal control topics with an emphasis on algorithm development, real world applications and numerical results. Participants from Canada, Japan, Sweden, The Netherlands, Germany, Belgium, Greece, and Denmark gave the meeting an important international component. At tendees also included representatives from IBM, American Airlines, US Air, United Parcel Serice, AT & T Bell Labs, Thinking Machines, Army High Performance Com puting Research Center, and Argonne National Laboratory. In addition, the NSF sponsored attendance of thirteen graduate students from universities in the United States and abroad. Accurate modeling of scientific problems often leads to the formulation of large scale optimization problems involving thousands of continuous and/or discrete vari ables. Large scale optimization has seen a dramatic increase in activities in the past decade. This has been a natural consequence of new algorithmic developments and of the increased power of computers. For example, decomposition ideas proposed by G. Dantzig and P. Wolfe in the 1960's, are now implement able in distributed process ing systems, and today many optimization codes have been implemented on parallel machines.

Author : Ramu Sharat Chandra
Publisher : Unknown
Page : 312 pages
File Size : 54,5 Mb
Release : 2006
Category : Electronic
ISBN : CORNELL:31924104714740

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Control of Large Scale Interconnected Systems by Ramu Sharat Chandra Pdf

Author : Nisheeth K. Vishnoi
Publisher : Cambridge University Press
Page : 314 pages
File Size : 54,9 Mb
Release : 2021-10-07
Category : Computers
ISBN : 9781108633994

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Algorithms for Convex Optimization by Nisheeth K. Vishnoi Pdf

In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.