Nonconvex Optimization and Its Applications

Handbook of Generalized Convexity and Generalized Monotonicity

Editors: Hadjisavvas, Nicolas, Komlósi, Sándor, Schaible, Siegfried S. (Eds.)

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About this Textbook

 

Various generalizations of the classical concept of a convex function have been introduced, especially during the second half of the 20th century. Generalized convex functions are the many nonconvex functions which share at least one of the valuable properties of convex functions. Apart from their theoretical interest, they are often more suitable than convex functions to describe real-word problems in disciplines such as economics, engineering, management science, probability theory and in other applied sciences. More recently, generalized monotone maps which are closely related to generalized convex functions have also been studied extensively. While initial efforts to generalize convexity and monotonicity were limited to only a few research centers, today there are numerous researchers throughout the world and in various disciplines engaged in theoretical and applied studies of generalized convexity/monotonicity (see http://www.genconv.org).

The Handbook offers a systematic and thorough exposition of the theory and applications of the various aspects of generalized convexity and generalized monotonicity. It is aimed at the non-expert, for whom it provides a detailed introduction, as well as at the expert who seeks to learn about the latest developments and references in his research area. Results in this fast growing field are contained in a large number of scientific papers which appeared in a variety of professional journals, partially due to the interdisciplinary nature of the subject matter. Each of its fourteen chapters is written by leading experts of the respective research area starting from the very basics and moving on to the state of the art of the subject.

Each chapter is complemented by a comprehensive bibliography which will assist the non-expert and expert alike.

Table of contents (14 chapters)

Table of contents (14 chapters)
  • Introduction to Convex and Quasiconvex Analysis

    Pages 3-87

    Frenk, Johannes B.G. (et al.)

  • Criteria for Generalized Convexity and Generalized Monotonicity in the Differentiable Case

    Pages 89-119

    Crouzeix, Jean-Pierre

  • Continuity and Differentiability of Quasiconvex Functions

    Pages 121-149

    Crouzeix, Jean-Pierre

  • Generalized Convexity and Optimality Conditions in Scalar and Vector Optimization

    Pages 151-193

    Alberto, Cambini (et al.)

  • Generalized Convexity in Vector Optimization

    Pages 195-236

    Dinh The, Luc

Buy this book

eBook $219.00
price for USA in USD (gross)
  • ISBN 978-0-387-23393-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $279.99
price for USA in USD
  • ISBN 978-0-387-23255-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $279.99
price for USA in USD
  • ISBN 978-1-4899-9502-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Handbook of Generalized Convexity and Generalized Monotonicity
Editors
  • Nicolas Hadjisavvas
  • Sándor Komlósi
  • Siegfried S. Schaible
Series Title
Nonconvex Optimization and Its Applications
Series Volume
76
Copyright
2005
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-23393-2
DOI
10.1007/b101428
Hardcover ISBN
978-0-387-23255-3
Softcover ISBN
978-1-4899-9502-5
Series ISSN
1571-568X
Edition Number
1
Number of Pages
XX, 672
Topics