Handbook of Generalized Convexity and Generalized Monotonicity

  • Nicolas Hadjisavvas
  • Sándor Komlósi
  • Siegfried Schaible

Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 76)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Generalized Convexity

    1. Johannes B.G. Frenk, Gábor Kassay
      Pages 3-87
    2. Juan Enrique Martínez-Legaz
      Pages 237-292
    3. Alexander Rubinov, Joydeep Dutta
      Pages 293-333
    4. Johannes B. G. Frenk, Siegfried Schaible
      Pages 335-386
  3. Generalized Monotonicity

  4. Back Matter
    Pages 667-672

About this book

Introduction

 

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.

Keywords

Convexity Vector optimization calculus derivative game theory optimization

Editors and affiliations

  • Nicolas Hadjisavvas
    • 1
  • Sándor Komlósi
    • 2
  • Siegfried Schaible
    • 3
  1. 1.University of AegeanGreece
  2. 2.University of PécsHungary
  3. 3.University of CaliforniaRiversideUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b101428
  • Copyright Information Springer Science + Business Media, Inc. 2005
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-23255-3
  • Online ISBN 978-0-387-23393-2
  • Series Print ISSN 1571-568X
  • About this book
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