Convex Functional Analysis
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Author | : Andrew J. Kurdila |
Publisher | : Springer Science & Business Media |
Total Pages | : 238 |
Release | : 2006-03-30 |
Genre | : Science |
ISBN | : 3764373571 |
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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 | : Andrew J. Kurdila |
Publisher | : Springer Science & Business Media |
Total Pages | : 246 |
Release | : 2005-05-23 |
Genre | : Science |
ISBN | : 9783764321987 |
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 |
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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 | : 430 |
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 | : 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 | : 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 | : Ralph Tyrell Rockafellar |
Publisher | : Princeton University Press |
Total Pages | : 470 |
Release | : 2015-04-29 |
Genre | : Mathematics |
ISBN | : 1400873177 |
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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 | : Andrew Kurdila |
Publisher | : Birkhauser |
Total Pages | : 228 |
Release | : 2005-01-01 |
Genre | : Convex functions |
ISBN | : 9780817621988 |
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 | : Semën Samsonovich Kutateladze |
Publisher | : Springer Science & Business Media |
Total Pages | : 289 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401587558 |
Download Fundamentals of Functional Analysis Book in PDF, Epub and Kindle
to the English Translation This is a concise guide to basic sections of modern functional analysis. Included are such topics as the principles of Banach and Hilbert spaces, the theory of multinormed and uniform spaces, the Riesz-Dunford holomorphic functional calculus, the Fredholm index theory, convex analysis and duality theory for locally convex spaces. With standard provisos the presentation is self-contained, exposing about a h- dred famous "named" theorems furnished with complete proofs and culminating in the Gelfand-Nalmark-Segal construction for C*-algebras. The first Russian edition was printed by the Siberian Division of "Nauka" P- lishers in 1983. Since then the monograph has served as the standard textbook on functional analysis at the University of Novosibirsk. This volume is translated from the second Russian edition printed by the Sobolev Institute of Mathematics of the Siberian Division of the Russian Academy of Sciences· in 1995. It incorporates new sections on Radon measures, the Schwartz spaces of distributions, and a supplementary list of theoretical exercises and problems. This edition was typeset using AMS-'lEX, the American Mathematical Society's 'lEX system. To clear my conscience completely, I also confess that := stands for the definor, the assignment operator, signifies the end of the proof.
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.