Duality For Nonconvex Approximation And Optimization
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Duality For Nonconvex Approximation And Optimization
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Author : Ivan Singer
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-12
Duality For Nonconvex Approximation And Optimization written by Ivan Singer 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 2007-03-12 with Mathematics categories.
The theory of convex optimization has been constantly developing over the past 30 years. Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimizaton problems. This manuscript contains an exhaustive presentation of the duality for these classes of problems and some of its generalization in the framework of abstract convexity. This manuscript will be of great interest for experts in this and related fields.
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.
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.
Introduction To The Theory Of Nonlinear Optimization
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Author : Johannes Jahn
language : en
Publisher: Springer Nature
Release Date : 2020-07-02
Introduction To The Theory Of Nonlinear Optimization written by Johannes Jahn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-02 with Business & Economics categories.
This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.
Approximation And Optimization Of Discrete And Differential Inclusions
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Author : Elimhan N Mahmudov
language : en
Publisher: Elsevier
Release Date : 2011-08-25
Approximation And Optimization Of Discrete And Differential Inclusions written by Elimhan N Mahmudov and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-25 with Mathematics categories.
Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions. In addition to including well-recognized results of variational analysis and optimization, the book includes a number of new and important ones Includes practical examples
Geometric Approximation Theory
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Author : Alexey R. Alimov
language : en
Publisher: Springer Nature
Release Date : 2022-03-29
Geometric Approximation Theory written by Alexey R. Alimov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-29 with Mathematics categories.
This monograph provides a comprehensive introduction to the classical geometric approximation theory, emphasizing important themes related to the theory including uniqueness, stability, and existence of elements of best approximation. It presents a number of fundamental results for both these and related problems, many of which appear for the first time in monograph form. The text also discusses the interrelations between main objects of geometric approximation theory, formulating a number of auxiliary problems for demonstration. Central ideas include the problems of existence and uniqueness of elements of best approximations as well as properties of sets including subspaces of polynomials and splines, classes of rational functions, and abstract subsets of normed linear spaces. The book begins with a brief introduction to geometric approximation theory, progressing through fundamental classical ideas and results as a basis for various approximation sets, suns, and Chebyshev systems. It concludes with a review of approximation by abstract sets and related problems, presenting novel results throughout the section. This text is suitable for both theoretical and applied viewpoints and especially researchers interested in advanced aspects of the field.
Biorthogonal Systems In Banach Spaces
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Author : Petr Hajek
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-04
Biorthogonal Systems In Banach Spaces written by Petr Hajek 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 2007-10-04 with Mathematics categories.
This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research.
Lectures On Modern Convex Optimization
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Author : Aharon Ben-Tal
language : fr
Publisher: SIAM
Release Date : 2001-01-01
Lectures On Modern Convex Optimization written by Aharon Ben-Tal and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Technology & Engineering categories.
Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.
Convex Analysis And Beyond
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Author : Boris S. Mordukhovich
language : en
Publisher: Springer Nature
Release Date : 2022-04-24
Convex Analysis And Beyond written by Boris S. Mordukhovich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-24 with Mathematics categories.
This book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications. The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classes in mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.