Infinite-Dimensional Optimization and Convexity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Infinite-Dimensional Optimization and Convexity write by Ivar Ekeland. This book was released on 1983-09-15. Infinite-Dimensional Optimization and Convexity available in PDF, EPUB and Kindle. The caratheodory approach; Infinite-dimensional optimization; Duality theory.
Convexity and Optimization in Banach Spaces
Convexity and Optimization in Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Convexity and Optimization in Banach Spaces write by Viorel Barbu. This book was released on 2012-01-03. Convexity and Optimization in Banach Spaces available in PDF, EPUB and Kindle. 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.
Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization
Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization write by D. Butnariu. This book was released on 2012-12-06. Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization available in PDF, EPUB and Kindle. The aim of this work is to present in a unified approach a series of results concerning totally convex functions on Banach spaces and their applications to building iterative algorithms for computing common fixed points of mea surable families of operators and optimization methods in infinite dimen sional settings. The notion of totally convex function was first studied by Butnariu, Censor and Reich [31] in the context of the space lRR because of its usefulness for establishing convergence of a Bregman projection method for finding common points of infinite families of closed convex sets. In this finite dimensional environment total convexity hardly differs from strict convexity. In fact, a function with closed domain in a finite dimensional Banach space is totally convex if and only if it is strictly convex. The relevancy of total convexity as a strengthened form of strict convexity becomes apparent when the Banach space on which the function is defined is infinite dimensional. In this case, total convexity is a property stronger than strict convexity but weaker than locally uniform convexity (see Section 1.3 below). The study of totally convex functions in infinite dimensional Banach spaces was started in [33] where it was shown that they are useful tools for extrapolating properties commonly known to belong to operators satisfying demanding contractivity requirements to classes of operators which are not even mildly nonexpansive.
Optimality Conditions in Convex Optimization
Optimality Conditions in Convex Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimality Conditions in Convex Optimization write by Anulekha Dhara. This book was released on 2011-10-17. Optimality Conditions in Convex Optimization available in PDF, EPUB and Kindle. 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.
Convex Analysis and Variational Problems
Convex Analysis and Variational Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Convex Analysis and Variational Problems write by Ivar Ekeland. This book was released on 1999-12-01. Convex Analysis and Variational Problems available in PDF, EPUB and Kindle. 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.
