Convex Optimization in Normed 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 Convex Optimization in Normed Spaces write by Juan Peypouquet. This book was released on 2015-03-18. Convex Optimization in Normed Spaces available in PDF, EPUB and Kindle. This work is intended to serve as a guide for graduate students and researchers who wish to get acquainted with the main theoretical and practical tools for the numerical minimization of convex functions on Hilbert spaces. Therefore, it contains the main tools that are necessary to conduct independent research on the topic. It is also a concise, easy-to-follow and self-contained textbook, which may be useful for any researcher working on related fields, as well as teachers giving graduate-level courses on the topic. It will contain a thorough revision of the extant literature including both classical and state-of-the-art references.
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.
Optimization in Function Spaces
Optimization in Function 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 Optimization in Function Spaces write by Peter Kosmol. This book was released on 2011-02-28. Optimization in Function Spaces available in PDF, EPUB and Kindle. This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. A particular emphasis is placed on the geometrical aspects of strong solvability of a convex optimization problem: it turns out that this property is equivalent to local uniform convexity of the corresponding convex function. This treatise also provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other. The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level. From the contents: Approximation and Polya Algorithms in Orlicz Spaces Convex Sets and Convex Functions Numerical Treatment of Non-linear Equations and Optimization Problems Stability and Two-stage Optimization Problems Orlicz Spaces, Orlicz Norm and Duality Differentiability and Convexity in Orlicz Spaces Variational Calculus
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.
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 1978. Convexity and Optimization in Banach Spaces available in PDF, EPUB and Kindle.
