Item description for Convex Functional Analysis (Systems & Control: Foundations & Applications) by Andrew J. Kurdila...
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.
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Est. Packaging Dimensions: Length: 9.4" Width: 6.3" Height: 0.7" Weight: 1.1 lbs.
Release Date Aug 10, 2005
Publisher Birkhäuser Basel
ISBN 3764321989 ISBN13 9783764321987
Availability 95 units. Availability accurate as of Mar 22, 2017 10:30.
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More About Andrew J. Kurdila
Andrew J. Kurdila has an academic affiliation as follows - University of Florida.
Reviews - What do customers think about Convex Functional Analysis (Systems & Control: Foundations & Applications)?
A great book of convex functional analysis, but not easy for beginners Jan 29, 2008
Professors Kurdila and Zabarankin have done a great job putting together several topics of functional analysis, measure theory, convex analysis and optimization. However, although this book was prepared following the idea to provide the minimum of the theory required to understand the principle of functional analysis and convex analysis, I believe that this book is not easy for beginners (self-study).
If you have already studied functional analysis (using for instance chapters 1,2, 3 and 4 of kreyszig), introductory topology (using for instance chapter 2 of Gamelin and Greene) and measure theory (using for instance Bartle), I strongly believe that you will enjoy this book.
Chapter 1, 2 and 3 the authors introduce the basics of topology, functional analysis, and measure theory.
Chapter 4 is fantastic. They introduce differential calculus in vector spaces. They also provide several examples that make a connection between the notions of differentiability on these spaces and classical differentiability.
Chapter 5, 6 and 7 provide the main objective of the book which is optimization. One drawback of these chapters is that there are no examples. However, you can get several examples of control theory and calculus of variations for this chapter elsewhere such as in Optimization by Vector Space Methods by David G. Luenberger and Introduction to the Calculus of variations by Hans Sagan.
Finally, since the topics of this book were carefully chosen, this book seems to be a great choice to be used as text book in a PhD course of optimization for mathematicians, engineers, economists and physicists.