Convex Optimization In Normed Spaces PDF Download
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Author | : Juan Peypouquet |
Publisher | : Springer |
Total Pages | : 132 |
Release | : 2015-03-18 |
Genre | : Mathematics |
ISBN | : 3319137107 |
Download Convex Optimization in Normed Spaces Book 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.
Author | : Viorel Barbu |
Publisher | : Springer Science & Business Media |
Total Pages | : 376 |
Release | : 2012-01-03 |
Genre | : Mathematics |
ISBN | : 940072246X |
Download Convexity and Optimization in Banach Spaces Book 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.
Author | : Peter Kosmol |
Publisher | : Walter de Gruyter |
Total Pages | : 405 |
Release | : 2011-02-28 |
Genre | : Mathematics |
ISBN | : 3110250217 |
Download Optimization in Function Spaces Book 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
Author | : D. Butnariu |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401140669 |
Download Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization Book 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.
Author | : Viorel Barbu |
Publisher | : Springer |
Total Pages | : 344 |
Release | : 1978 |
Genre | : Juvenile Nonfiction |
ISBN | : |
Download Convexity and Optimization in Banach Spaces Book in PDF, ePub and Kindle
Author | : Miroslav Bacak |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 217 |
Release | : 2014-10-29 |
Genre | : Mathematics |
ISBN | : 3110391082 |
Download Convex Analysis and Optimization in Hadamard Spaces Book in PDF, ePub and Kindle
In the past two decades, convex analysis and optimization have been developed in Hadamard spaces. This book represents a first attempt to give a systematic account on the subject. Hadamard spaces are complete geodesic spaces of nonpositive curvature. They include Hilbert spaces, Hadamard manifolds, Euclidean buildings and many other important spaces. While the role of Hadamard spaces in geometry and geometric group theory has been studied for a long time, first analytical results appeared as late as in the 1990s. Remarkably, it turns out that Hadamard spaces are appropriate for the theory of convex sets and convex functions outside of linear spaces. Since convexity underpins a large number of results in the geometry of Hadamard spaces, we believe that its systematic study is of substantial interest. Optimization methods then address various computational issues and provide us with approximation algorithms which may be useful in sciences and engineering. We present a detailed description of such an application to computational phylogenetics. The book is primarily aimed at both graduate students and researchers in analysis and optimization, but it is accessible to advanced undergraduate students as well.
Author | : Alexander J. Zaslavski |
Publisher | : Springer Science & Business Media |
Total Pages | : 443 |
Release | : 2010-08-05 |
Genre | : Mathematics |
ISBN | : 0387886214 |
Download Optimization on Metric and Normed Spaces Book in PDF, ePub and Kindle
"Optimization on Metric and Normed Spaces" is devoted to the recent progress in optimization on Banach spaces and complete metric spaces. Optimization problems are usually considered on metric spaces satisfying certain compactness assumptions which guarantee the existence of solutions and convergence of algorithms. This book considers spaces that do not satisfy such compactness assumptions. In order to overcome these difficulties, the book uses the Baire category approach and considers approximate solutions. Therefore, it presents a number of new results concerning penalty methods in constrained optimization, existence of solutions in parametric optimization, well-posedness of vector minimization problems, and many other results obtained in the last ten years. The book is intended for mathematicians interested in optimization and applied functional analysis.
Author | : C. Zalinescu |
Publisher | : World Scientific |
Total Pages | : 389 |
Release | : 2002 |
Genre | : Science |
ISBN | : 9812380671 |
Download Convex Analysis in General Vector Spaces Book in PDF, ePub and Kindle
The primary aim of this book is to present the conjugate and sub/differential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions, uniformly convex and uniformly smooth convex functions, best approximation problems, characterizations of convexity, the study of the sets of weak sharp minima, well-behaved functions and the existence of global error bounds for convex inequalities, as well as the study of monotone multifunctions by using convex functions.
Author | : Ivan Singer |
Publisher | : Springer Science & Business Media |
Total Pages | : 366 |
Release | : 2007-03-12 |
Genre | : Mathematics |
ISBN | : 0387283951 |
Download Duality for Nonconvex Approximation and Optimization Book in PDF, ePub and Kindle
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.
Author | : Boris S. Mordukhovich |
Publisher | : Springer Nature |
Total Pages | : 597 |
Release | : 2022-04-24 |
Genre | : Mathematics |
ISBN | : 3030947858 |
Download Convex Analysis and Beyond Book in PDF, ePub and Kindle
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.