Large Scale Convex Optimization
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Large Scale Convex Optimization
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Author : Ernest K. Ryu
language : en
Publisher: Cambridge University Press
Release Date : 2022-12-01
Large Scale Convex Optimization written by Ernest K. Ryu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-01 with Mathematics categories.
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.
Large Scale And Distributed Optimization
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Author : Pontus Giselsson
language : en
Publisher: Springer
Release Date : 2018-11-11
Large Scale And Distributed Optimization written by Pontus Giselsson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-11 with Mathematics categories.
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.
Large Scale Optimization
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Author : Vladimir Tsurkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Large Scale Optimization written by Vladimir Tsurkov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Computers categories.
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.
Large Scale Optimization In Supply Chains And Smart Manufacturing
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Author : Jesús M. Velásquez-Bermúdez
language : en
Publisher: Springer Nature
Release Date : 2019-09-06
Large Scale Optimization In Supply Chains And Smart Manufacturing written by Jesús M. Velásquez-Bermúdez and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-06 with Mathematics categories.
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.
Convex Optimization Algorithms
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Author : Dimitri Bertsekas
language : en
Publisher: Athena Scientific
Release Date : 2015-02-01
Convex Optimization Algorithms written by Dimitri Bertsekas and has been published by Athena Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-01 with Mathematics categories.
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.
Convex Optimization Theory
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Author : Dimitri Bertsekas
language : en
Publisher: Athena Scientific
Release Date : 2009-06-01
Convex Optimization Theory written by Dimitri Bertsekas and has been published by Athena Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-01 with Mathematics categories.
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).
Large Scale Numerical Optimization
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Author : Thomas Frederick Coleman
language : en
Publisher: SIAM
Release Date : 1990-01-01
Large Scale Numerical Optimization written by Thomas Frederick Coleman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
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.
Online Optimization Of Large Scale Systems
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Author : Martin Grötschel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Online Optimization Of Large Scale Systems written by Martin Grötschel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
In its thousands of years of history, mathematics has made an extraordinary ca reer. It started from rules for bookkeeping and computation of areas to become the language of science. Its potential for decision support was fully recognized in the twentieth century only, vitally aided by the evolution of computing and communi cation technology. Mathematical optimization, in particular, has developed into a powerful machinery to help planners. Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision making. Opti mization is particularly strong if precise models of real phenomena and data of high quality are at hand - often yielding reliable automated control and decision proce dures. But what, if the models are soft and not all data are around? Can mathematics help as well? This book addresses such issues, e. g. , problems of the following type: - An elevator cannot know all transportation requests in advance. In which order should it serve the passengers? - Wing profiles of aircrafts influence the fuel consumption. Is it possible to con tinuously adapt the shape of a wing during the flight under rapidly changing conditions? - Robots are designed to accomplish specific tasks as efficiently as possible. But what if a robot navigates in an unknown environment? - Energy demand changes quickly and is not easily predictable over time. Some types of power plants can only react slowly.
Optimization Methods For Large Scale Systems With Applications
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Author : David A. Wismer
language : en
Publisher: McGraw-Hill Companies
Release Date : 1971
Optimization Methods For Large Scale Systems With Applications written by David A. Wismer and has been published by McGraw-Hill Companies this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Control Of Large Scale Interconnected Systems
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Author : Ramu Sharat Chandra
language : en
Publisher:
Release Date : 2006
Control Of Large Scale Interconnected Systems written by Ramu Sharat Chandra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.