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Generalized Convexity, Generalized Monotonicity: Recent Results

Recent Results

  • Book
  • © 1998
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Overview

Editors:
  1. Jean-Pierre Crouzeix

    1. Université Blaise Pascal, Clermont-Ferrand, France

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    You can also search for this editor in PubMed   Google Scholar

  2. Juan-Enrique Martinez-Legaz

    1. Universitat Autònoma de Barcelona, Barcelona, Spain

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    You can also search for this editor in PubMed   Google Scholar

  3. Michel Volle

    1. Université d’Avignon, Avignon, France

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Nonconvex Optimization and Its Applications (NOIA, volume 27)

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Table of contents (23 chapters)

  1. Front Matter

    Pages i-xv
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  2. Generalized Convexity

    1. Front Matter

      Pages 1-1
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    2. Are Generalized Derivatives Sseful for Generalized Convex Functions?

      • Jean-Paul Penot
      Pages 3-59
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    3. Stochastic Programs with Chance Constraints: Generalized Convexity and Approximation Issues

      • Roger J-B Wets
      Pages 61-74
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    4. Error Bounds for Convex Inequality Systems

      • Adrian S. Lewis, Jong-Shi Pang
      Pages 75-110
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    5. Applying Generalised Convexity Notions to Jets

      • Andrew Eberhard, Michael Nyblom, Danny Ralph
      Pages 111-157
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    6. Quasiconvexity via Two Step Functions

      • A. M. Rubinov, B. M. Glover
      Pages 159-183
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    7. On Limiting Fréchet ε-Subdifferentials

      • A. Jourani, M. Théra
      Pages 185-198
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    8. Convexity Space with Respect to a Given Set

      • Lucia Blaga, Liana Lupşa
      Pages 199-208
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    9. A Convexity Condition for the Nonexistence of Some Antiproximinal Sets in the Space of Integrable Functions

      • Anca-Maria Precupanu
      Pages 209-217
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    10. Characterizations of ρ-Convex Functions

      • Marco Castellani, Massimo Pappalardo
      Pages 219-233
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  4. Optimality Conditions and Duality

    1. Front Matter

      Pages 303-303
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    2. Simplified Global Optimality Conditions in Generalized Conjugation Theory

      • Fabián Flores-Bazán, Juan-Enrique Martínez-Legaz
      Pages 305-329
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    3. Duality in DC Programming

      • B. Lemaire, M. Volle
      Pages 331-345
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    4. Recent Developments in Second Order Necessary Optimality Conditions

      • Alberto Cambini, Sándor Komlósi, Laura Martein
      Pages 347-356
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Keywords

About this book

A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo­ metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man­ agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized convexity off unctions as monotonicity relates to convexity. Generalized monotonicity plays a role in variational inequality problems, complementarity problems and more generally, in equilibrium prob­ lems.

Editors and Affiliations

  • Université Blaise Pascal, Clermont-Ferrand, France

    Jean-Pierre Crouzeix

  • Universitat Autònoma de Barcelona, Barcelona, Spain

    Juan-Enrique Martinez-Legaz

  • Université d’Avignon, Avignon, France

    Michel Volle

Bibliographic Information

  • Book Title: Generalized Convexity, Generalized Monotonicity: Recent Results

  • Book Subtitle: Recent Results

  • Editors: Jean-Pierre Crouzeix, Juan-Enrique Martinez-Legaz, Michel Volle

  • Series Title: Nonconvex Optimization and Its Applications

  • DOI: https://doi.org/10.1007/978-1-4613-3341-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Kluwer Academic Publishers 1998

  • Hardcover ISBN: 978-0-7923-5088-0Published: 31 August 1998

  • Softcover ISBN: 978-1-4613-3343-2Published: 12 October 2011

  • eBook ISBN: 978-1-4613-3341-8Published: 01 December 2013

  • Series ISSN: 1571-568X

  • Edition Number: 1

  • Number of Pages: XVI, 471

  • Topics: Optimization, Economic Theory/Quantitative Economics/Mathematical Methods, Econometrics

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