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Springer Monographs in Mathematics

Asymptotic Cones and Functions in Optimization and Variational Inequalities

Authors: Auslender, Alfred, Teboulle, Marc

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  • ISBN 978-0-387-22590-6
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Hardcover $139.99
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Softcover $139.99
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  • ISBN 978-1-4419-3036-1
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About this book

Nonlinear applied analysis and in particular the related ?elds of continuous optimization and variational inequality problems have gone through major developments over the last three decades and have reached maturity. A pivotal role in these developments has been played by convex analysis, a rich area covering a broad range of problems in mathematical sciences and its applications. Separation of convex sets and the Legendre–Fenchel conjugate transforms are fundamental notions that have laid the ground for these fruitful developments. Two other fundamental notions that have contributed to making convex analysis a powerful analytical tool and that haveoftenbeenhiddeninthesedevelopmentsarethenotionsofasymptotic sets and functions. The purpose of this book is to provide a systematic and comprehensive account of asymptotic sets and functions, from which a broad and u- ful theory emerges in the areas of optimization and variational inequa- ties. There is a variety of motivations that led mathematicians to study questions revolving around attaintment of the in?mum in a minimization problem and its stability, duality and minmax theorems, convexi?cation of sets and functions, and maximal monotone maps. In all these topics we are faced with the central problem of handling unbounded situations.

Reviews

From the reviews:

"The main purpose of this book is to provide a systematic study of asymptotic cones and asymptotic functions in finite dimensional normed spaces. … Every chapter ends with bibliographical notes. … The book is addressed to graduate students at an advanced level and to researchers and practitioners in the fields of optimization theory, nonlinear programming and applied mathematical sciences. ... We recommend this book to all those who are interested in asymptotic analysis and its use." (Constantin Zalinescu, Zentralblatt MATH, Vol. 1017, 2003)


Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-0-387-22590-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-0-387-95520-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.99
price for USA in USD
  • ISBN 978-1-4419-3036-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Asymptotic Cones and Functions in Optimization and Variational Inequalities
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2003
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-387-22590-6
DOI
10.1007/b97594
Hardcover ISBN
978-0-387-95520-9
Softcover ISBN
978-1-4419-3036-1
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XII, 249
Topics