Convex Functional Analysis PDF Download
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Author | : Andrew J. Kurdila |
Publisher | : Springer Science & Business Media |
Total Pages | : 238 |
Release | : 2006-03-30 |
Genre | : Science |
ISBN | : 3764373571 |
Download Convex Functional Analysis Book in PDF, ePub and Kindle
This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems.
Author | : Steven G. Krantz |
Publisher | : CRC Press |
Total Pages | : 174 |
Release | : 2014-10-20 |
Genre | : Mathematics |
ISBN | : 149870638X |
Download Convex Analysis Book in PDF, ePub and Kindle
Convexity is an ancient idea going back to Archimedes. Used sporadically in the mathematical literature over the centuries, today it is a flourishing area of research and a mathematical subject in its own right. Convexity is used in optimization theory, functional analysis, complex analysis, and other parts of mathematics.Convex Analysis introduces
Author | : Constantin P. Niculescu |
Publisher | : Springer |
Total Pages | : 415 |
Release | : 2018-06-08 |
Genre | : Mathematics |
ISBN | : 3319783378 |
Download Convex Functions and Their Applications Book in PDF, ePub and Kindle
Thorough introduction to an important area of mathematics Contains recent results Includes many exercises
Author | : L. Asimow |
Publisher | : Elsevier |
Total Pages | : 277 |
Release | : 2014-06-28 |
Genre | : Mathematics |
ISBN | : 1483294692 |
Download Convexity Theory and its Applications in Functional Analysis Book in PDF, ePub and Kindle
Convexity Theory Appl Functional Analysis
Author | : Fabio Botelho |
Publisher | : Springer |
Total Pages | : 584 |
Release | : 2014-06-12 |
Genre | : Mathematics |
ISBN | : 3319060740 |
Download Functional Analysis and Applied Optimization in Banach Spaces Book in PDF, ePub and Kindle
This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
Author | : Ralph Tyrell Rockafellar |
Publisher | : Princeton University Press |
Total Pages | : 470 |
Release | : 2015-04-29 |
Genre | : Mathematics |
ISBN | : 1400873177 |
Download Convex Analysis Book in PDF, ePub and Kindle
Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle- functions. This book has firmly established a new and vital area not only for pure mathematics but also for applications to economics and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. There is also a guide for the reader who may be using the book as an introduction, indicating which parts are essential and which may be skipped on a first reading.
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 | : Jonathan Borwein |
Publisher | : Springer Science & Business Media |
Total Pages | : 316 |
Release | : 2010-05-05 |
Genre | : Mathematics |
ISBN | : 0387312560 |
Download Convex Analysis and Nonlinear Optimization Book in PDF, ePub and Kindle
Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.
Author | : R. B. Holmes |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2012-12-12 |
Genre | : Mathematics |
ISBN | : 9781468493719 |
Download Geometric Functional Analysis and its Applications Book in PDF, ePub and Kindle
This book has evolved from my experience over the past decade in teaching and doing research in functional analysis and certain of its appli cations. These applications are to optimization theory in general and to best approximation theory in particular. The geometric nature of the subjects has greatly influenced the approach to functional analysis presented herein, especially its basis on the unifying concept of convexity. Most of the major theorems either concern or depend on properties of convex sets; the others generally pertain to conjugate spaces or compactness properties, both of which topics are important for the proper setting and resolution of optimization problems. In consequence, and in contrast to most other treatments of functional analysis, there is no discussion of spectral theory, and only the most basic and general properties of linear operators are established. Some of the theoretical highlights of the book are the Banach space theorems associated with the names of Dixmier, Krein, James, Smulian, Bishop-Phelps, Brondsted-Rockafellar, and Bessaga-Pelczynski. Prior to these (and others) we establish to two most important principles of geometric functional analysis: the extended Krein-Milman theorem and the Hahn Banach principle, the latter appearing in ten different but equivalent formula tions (some of which are optimality criteria for convex programs). In addition, a good deal of attention is paid to properties and characterizations of conjugate spaces, especially reflexive spaces.
Author | : Kosaku Yosida |
Publisher | : Springer Science & Business Media |
Total Pages | : 480 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662117916 |
Download Functional Analysis Book in PDF, ePub and Kindle