New Duality Results For Separable Optimization Problems In Infinite Dimensions
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New Duality Results For Separable Optimization Problems In Infinite Dimensions
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Author : Saba Naser Majeed
language : en
Publisher:
Release Date : 2013
New Duality Results For Separable Optimization Problems In Infinite Dimensions written by Saba Naser Majeed and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Control theory categories.
A Duality Approach To Gap Functions For Variational Inequalities And Equilibrium Problems
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Author :
language : en
Publisher:
Release Date : 2006
A Duality Approach To Gap Functions For Variational Inequalities And Equilibrium Problems written by 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.
This work aims to investigate some applications of the conjugate duality for scalar and vector optimization problems to the construction of gap functions for variational inequalities and equilibrium problems. The basic idea of the approach is to reformulate variational inequalities and equilibrium problems into optimization problems depending on a fixed variable, which allows us to apply duality results from optimization problems. Based on some perturbations, first we consider the conjugate duality for scalar optimization. As applications, duality investigations for the convex partially separable optimization problem are discussed. Afterwards, we concentrate our attention on some applications of conjugate duality for convex optimization problems in finite and infinite-dimensional spaces to the construction of a gap function for variational inequalities and equilibrium problems. To verify the properties in the definition of a gap function weak and strong duality are used. The remainder of this thesis deals with the extension of this approach to vector variational inequalities and vector equilibrium problems. By using the perturbation functions in analogy to the scalar case, different dual problems for vector optimization and duality assertions for these problems are derived. This study allows us to propose some set-valued gap functions for the vector variational inequality. Finally, by applying the Fenchel duality on the basis of weak orderings, some variational principles for vector equilibrium problems are investigated.
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.
Conjugate Duality And Optimization
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Author : R. Tyrrell Rockafellar
language : en
Publisher: SIAM
Release Date : 1974-01-01
Conjugate Duality And Optimization written by R. Tyrrell Rockafellar and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-01-01 with Technology & Engineering categories.
Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.
Duality In Optimization And Variational Inequalities
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Author : C.j. Goh
language : en
Publisher: Taylor & Francis
Release Date : 2002-05-10
Duality In Optimization And Variational Inequalities written by C.j. Goh and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-10 with Mathematics categories.
This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality. It provides a wider appreciation of optimality conditions in various scenarios and under different assumptions. It will enable the reader to use duality to devise more effective computational methods, and to aid more meaningful interpretation of optimization and variational inequality problems.
Stochastic Analysis Control Optimization And Applications
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Author : William M. McEneaney
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic Analysis Control Optimization And Applications written by William M. McEneaney 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 Technology & Engineering categories.
In view of Professor Wendell Fleming's many fundamental contributions, his profound influence on the mathematical and systems theory communi ties, his service to the profession, and his dedication to mathematics, we have invited a number of leading experts in the fields of control, optimiza tion, and stochastic systems to contribute to this volume in his honor on the occasion of his 70th birthday. These papers focus on various aspects of stochastic analysis, control theory and optimization, and applications. They include authoritative expositions and surveys as well as research papers on recent and important issues. The papers are grouped according to the following four major themes: (1) large deviations, risk sensitive and Hoc control, (2) partial differential equations and viscosity solutions, (3) stochastic control, filtering and parameter esti mation, and (4) mathematical finance and other applications. We express our deep gratitude to all of the authors for their invaluable contributions, and to the referees for their careful and timely reviews. We thank Harold Kushner for having graciously agreed to undertake the task of writing the foreword. Particular thanks go to H. Thomas Banks for his help, advice and suggestions during the entire preparation process, as well as for the generous support of the Center for Research in Scientific Computation. The assistance from the Birkhauser professional staff is also greatly appreciated.
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.
Optimization By Vector Space Methods
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Author : David G. Luenberger
language : en
Publisher: John Wiley & Sons
Release Date : 1997-01-23
Optimization By Vector Space Methods written by David G. Luenberger and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-23 with Technology & Engineering categories.
Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.
Nonlinear Programming
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Author : Dimitri Bertsekas
language : en
Publisher: Athena Scientific
Release Date : 2016-09-01
Nonlinear Programming 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 2016-09-01 with Mathematics categories.
This book provides a comprehensive and accessible presentation of algorithms for solving continuous optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. It 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 3rd edition brings the book in closer harmony with the companion works Convex Optimization Theory (Athena Scientific, 2009), Convex Optimization Algorithms (Athena Scientific, 2015), Convex Analysis and Optimization (Athena Scientific, 2003), and Network Optimization (Athena Scientific, 1998). These works are complementary in that they deal primarily with convex, possibly nondifferentiable, optimization problems and rely on convex analysis. By contrast the nonlinear programming book focuses primarily on analytical and computational methods for possibly nonconvex differentiable problems. It relies primarily on calculus and variational analysis, yet it still contains a detailed presentation of duality theory and its uses for both convex and nonconvex problems. This on-line edition contains detailed solutions to all the theoretical book exercises. Among its special features, the book: Provides extensive coverage of iterative optimization methods within a unifying framework Covers in depth duality theory from both a variational and a geometric point of view Provides a detailed treatment of interior point methods for linear programming Includes much new material on a number of topics, such as proximal algorithms, alternating direction methods of multipliers, and conic programming Focuses on large-scale optimization topics of much current interest, such as first order methods, incremental methods, and distributed asynchronous computation, and their applications in machine learning, signal processing, neural network training, and big data applications Includes a large number of examples and exercises Was developed through extensive classroom use in first-year graduate courses
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2007
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.