Convex Functional Analysis (Hardcover)

Andrew J. Kurdila

ISBN 10: 3764321989 / ISBN 13: 9783764321987

Published by Birkhauser Verlag AG, Basel, 2005

About this Item

Hardcover. The book is dedicated to functional and convex analysis techniques for the study of recent problems in optimal control and mechanics. It provides a rigorous foundation for the application of variational principles. Through the unifying approach of convex analysis, the text discusses four general types of applications: contact problems in mechanics, control of distributed parameter systems, control of incompressible flow, and identification problems in mechanics. It also considers extensions of convex analysis with application to the homogenization of steady state heat conduction equations, approximation theory in identification problems, and nonconvex variational problems in mechanics. Special emphasis is given to techniques for solving convex optimization problems subject to constraints. Overview of Book This book evolved over a period of years as the authors taught classes in var- tional calculus and applied functional analysis to graduatestudents in engineering and mathematics. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9783764321987

Bibliographic Details

• Title: Convex Functional Analysis (Hardcover)
• Publisher: Birkhauser Verlag AG, Basel
• Publication Date: 2005
• Language: English
• ISBN 10: 3764321989
• ISBN 13: 9783764321987
• Binding: Hardcover
• Condition: new

About this title

Synopsis

Overview of Book This book evolved over a period of years as the authors taught classes in var- tional calculus and applied functional analysis to graduatestudents in engineering and mathematics. The book has likewise been in?uenced by the authors’ research programs that have relied on the application of functional analytic principles to problems in variational calculus, mechanics and control theory. One of the most di?cult tasks in preparing to utilize functional, convex, and set-valued analysis in practical problems in engineering and physics is the inti- dating number of de?nitions, lemmas, theorems and propositions that constitute thefoundationsoffunctionalanalysis. Itcannotbeoveremphasizedthatfunctional analysis can be a powerful tool for analyzing practical problems in mechanics and physics. However, many academicians and researchers spend their lifetime stu- ing abstract mathematics. It is a demanding ?eld that requires discipline and devotion. It is a trite analogy that mathematics can be viewed as a pyramid of knowledge, that builds layer upon layer as more mathematical structure is put in place. The di?culty lies in the fact that an engineer or scientist typically would like to start somewhere “above the base” of the pyramid. Engineers and scientists are not as concerned, generally speaking, with the subtleties of deriving theorems axiomatically. Rather, they are interested in gaining a working knowledge of the applicability of the theory to their ?eld of interest.

From the Back Cover

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.

Contents:
Classical Abstract Spaces in Functional Analysis
Linear Functionals and Linear Operators
Common Function Spaces in Applications
Differential Calculus in Normed Vector Spaces
Minimization of Functionals
Convex Functionals
Lower Semicontinuous Functionals