Finite Dimensional Convexity And Optimization
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Finite Dimensional Convexity And Optimization
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Author : Monique Florenzano
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Finite Dimensional Convexity And Optimization written by Monique Florenzano 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 2012-12-06 with Mathematics categories.
This book discusses convex analysis, the basic underlying structure of argumentation in economic theory. Convex analysis is also common to the optimization of problems encountered in many applications. The text is aimed at senior undergraduate students, graduate students, and specialists of mathematical programming who are undertaking research into applied mathematics and economics. The text consists of a systematic development in eight chapters, and contains exercises. The book is appropriate as a class text or for self-study.
Convexity And Optimization In Finite Dimensions I
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Author : Josef Stoer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Convexity And Optimization In Finite Dimensions I written by Josef Stoer 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 2012-12-06 with Mathematics categories.
Dantzig's development of linear programming into one of the most applicable optimization techniques has spread interest in the algebra of linear inequalities, the geometry of polyhedra, the topology of convex sets, and the analysis of convex functions. It is the goal of this volume to provide a synopsis of these topics, and thereby the theoretical back ground for the arithmetic of convex optimization to be treated in a sub sequent volume. The exposition of each chapter is essentially independent, and attempts to reflect a specific style of mathematical reasoning. The emphasis lies on linear and convex duality theory, as initiated by Gale, Kuhn and Tucker, Fenchel, and v. Neumann, because it represents the theoretical development whose impact on modern optimi zation techniques has been the most pronounced. Chapters 5 and 6 are devoted to two characteristic aspects of duality theory: conjugate functions or polarity on the one hand, and saddle points on the other. The Farkas lemma on linear inequalities and its generalizations, Motzkin's description of polyhedra, Minkowski's supporting plane theorem are indispensable elementary tools which are contained in chapters 1, 2 and 3, respectively. The treatment of extremal properties of polyhedra as well as of general convex sets is based on the far reaching work of Klee. Chapter 2 terminates with a description of Gale diagrams, a recently developed successful technique for exploring polyhedral structures.
Optimality Conditions In Convex Optimization
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Author : Anulekha Dhara
language : en
Publisher: CRC Press
Release Date : 2011-10-17
Optimality Conditions In Convex Optimization written by Anulekha Dhara and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-17 with Business & Economics categories.
Optimality Conditions in Convex Optimization explores an important and central issue in the field of convex optimization: optimality conditions. It brings together the most important and recent results in this area that have been scattered in the literature—notably in the area of convex analysis—essential in developing many of the important results in this book, and not usually found in conventional texts. Unlike other books on convex optimization, which usually discuss algorithms along with some basic theory, the sole focus of this book is on fundamental and advanced convex optimization theory. Although many results presented in the book can also be proved in infinite dimensions, the authors focus on finite dimensions to allow for much deeper results and a better understanding of the structures involved in a convex optimization problem. They address semi-infinite optimization problems; approximate solution concepts of convex optimization problems; and some classes of non-convex problems which can be studied using the tools of convex analysis. They include examples wherever needed, provide details of major results, and discuss proofs of the main results.
Optimality Conditions In Convex Optimization
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Author : Anulekha Dhara
language : en
Publisher: CRC Press
Release Date : 2011-10-17
Optimality Conditions In Convex Optimization written by Anulekha Dhara and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-17 with Business & Economics categories.
Optimality Conditions in Convex Optimization explores an important and central issue in the field of convex optimization: optimality conditions. It brings together the most important and recent results in this area that have been scattered in the literature-notably in the area of convex analysis-essential in developing many of the important results
Convex Optimization
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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08
Convex Optimization written by Stephen P. Boyd 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 2004-03-08 with Business & Economics categories.
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.
Convexity And Optimization In Banach Spaces
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Author : Viorel Barbu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-03
Convexity And Optimization In Banach Spaces written by Viorel Barbu 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 2012-01-03 with Mathematics categories.
An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application. This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems. Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.
Foundations Of Optimization
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Author : Osman Güler
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-03
Foundations Of Optimization written by Osman Güler 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 2010-08-03 with Business & Economics categories.
This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with.
Convex Analysis And Variational Problems
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Author : Ivar Ekeland
language : en
Publisher: SIAM
Release Date : 1999-12-01
Convex Analysis And Variational Problems written by Ivar Ekeland and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-01 with Mathematics categories.
This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.
Convex Analysis And Nonlinear Optimization
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Author : Jonathan M. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-30
Convex Analysis And Nonlinear Optimization written by Jonathan M. Borwein 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 2005-11-30 with Mathematics categories.
Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.