Graduate Texts in Mathematics

Optima and Equilibria

An Introduction to Nonlinear Analysis

Authors: Aubin, Jean-Pierre

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  • ISBN 978-3-662-03539-9
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Hardcover $99.00
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About this Textbook

Advances in game theory and economic theory have proceeded hand in hand with that of nonlinear analysis and in particular, convex analysis. These theories motivated mathematicians to provide mathematical tools to deal with optima and equilibria. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its applications to economics and game theory, has written a rigorous and concise-yet still elementary and self-contained- text-book to present mathematical tools needed to solve problems motivated by economics, management sciences, operations research, cooperative and noncooperative games, fuzzy games, etc. It begins with convex and nonsmooth analysis,the foundations of optimization theory and mathematical programming. Nonlinear analysis is next presented in the context of zero-sum games and then, in the framework of set-valued analysis. These results are applied to the main classes of economic equilibria. The text continues with game theory: noncooperative (Nash) equilibria, Pareto optima, core and finally, fuzzy games. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses. -(See cont. News remarks)

Reviews

From the reviews:

MATHEMATICAL REVIEWS

"…provides a concise and self-contained exposition of the fundamental results both in the theory and its applications…Overall, the book presents a fundamental introduction to nonlinear analysis and its economic and game-theoretic applications. It can serve as a basic textbook for students and researchers interested in these areas."


Table of contents (17 chapters)

  • Introduction

    Aubin, Jean-Pierre

    Pages 1-6

  • Minimisation Problems: General Theorems

    Aubin, Jean-Pierre

    Pages 9-19

  • Convex Functions and Proximation, Projection and Separation Theorems

    Aubin, Jean-Pierre

    Pages 21-34

  • Conjugate Functions and Convex Minimisation Problems

    Aubin, Jean-Pierre

    Pages 35-56

  • Subdifferentials of Convex Functions

    Aubin, Jean-Pierre

    Pages 57-73

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-662-03539-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-3-540-64983-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • ISBN 978-3-642-08446-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Optima and Equilibria
Book Subtitle
An Introduction to Nonlinear Analysis
Authors
Translated by
Wilson, S.
Series Title
Graduate Texts in Mathematics
Series Volume
140
Copyright
1998
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-03539-9
DOI
10.1007/978-3-662-03539-9
Hardcover ISBN
978-3-540-64983-0
Softcover ISBN
978-3-642-08446-1
Series ISSN
0072-5285
Edition Number
2
Number of Pages
XVII, 433
Topics