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Generalized Convexity and Fractional Programming with Economic Applications

Proceedings of the International Workshop on “Generalized Concavity, Fractional Programming and Economic Applications” Held at the University of Pisa, Italy, May 30 – June 1, 1988

  • Conference proceedings
  • © 1990

Overview

Editors:
  1. Alberto Cambini

    1. Department of Statistics and Applied Mathematics, University of Pisa, Pisa, Italy

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  2. Erio Castagnoli

    1. Institute of Quantitative Methods, Bocconi University, Milano, Italy

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  3. Laura Martein

    1. Department of Statistics and Applied Mathematics, University of Pisa, Pisa, Italy

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  4. Piera Mazzoleni

    1. Institute of Mathematics, University of Verona, Verona, Italy

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  5. Siegfried Schaible

    1. Graduate School of Management, University of California, Riverside, USA

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 345)

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Table of contents (26 papers)

  1. Front Matter

    Pages N2-VII
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  2. Generalized Convexity

    1. Front Matter

      Pages 1-1
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    2. Introduction to Generalized Convexity

      • S. Schaible
      Pages 2-13

    3. Structural Developments of Concavity Properties

      • P. Mazzoleni
      Pages 14-22

    4. Projectively-Convex Models in Economics

      • S. T. Hackman, U. Passy
      Pages 23-35

    5. Convex Directional Derivatives in Optimization

      • D. Ward
      Pages 36-51

    6. Differentiable (α, λ) - Concave Functions

      • E. Castagnoli, P. Mazzoleni
      Pages 52-76

    7. On the Bicriteria Maximization Problem

      • L. Martein
      Pages 77-84

  3. Fractional Programming

    1. Front Matter

      Pages 85-85
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    2. Fractional Programming-Some Recent Results

      • C. R. Bector, A. Cambini
      Pages 86-98

    3. Recent Results in Disjunctive Linear Fractional Programming

      • V. Patkar, I. M. Stancu-Minasian
      Pages 99-105

    4. An Interval-Type Algorithm for Generalized Fractional Programming

      • Y. Benadada, J. P. Crouzeix, J. A. Ferland
      Pages 106-120

    5. A Modified Kelley’s Cutting Plane Algorithm for Some Special Nonconvex Problems

      • E. A. Sideri
      Pages 121-142

    6. Equivalence and parametric analysis in linear fractional programming

      • C. Sodini
      Pages 143-154

    7. Linear Fractional and Bicriteria Linear Fractional Programs

      • A. Cambini, L. Martein
      Pages 155-166

  4. Duality and Conjugation

    1. Front Matter

      Pages 167-167
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    2. Generalized Conjugation and Related Topics

      • J. E. Martinez-Legaz
      Pages 168-197

    3. On Strongly Convex and Paraconvex Dualities

      • J. P. Penot, M. Volle
      Pages 198-218

    4. Generalized Convexity and Fractional Optimization

      • K. H. Elster, A. Wolf
      Pages 219-231

    5. Duality in Multiobjective Fractional Programming

      • C. R. Bector, S. Chandra, C. Singh
      Pages 232-241
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Keywords

About this book

Generalizations of convex functions have been used in a variety of fields such as economics. business administration. engineering. statistics and applied sciences.· In 1949 de Finetti introduced one of the fundamental of generalized convex functions characterized by convex level sets which are now known as quasiconvex functions. Since then numerous types of generalized convex functions have been defined in accordance with the need of particular applications.· In each case such functions preserve soine of the valuable properties of a convex function. In addition to generalized convex functions this volume deals with fractional programs. These are constrained optimization problems which in the objective function involve one or several ratios. Such functions are often generalized convex. Fractional programs arise in management science. economics and numerical mathematics for example. In order to promote the circulation and development of research in this field. an international workshop on "Generalized Concavity. Fractional Programming and Economic Applications" was held at the University of Pisa. Italy. May 30 - June 1. 1988. Following conferences on similar topics in Vancouver. Canada in 1980 and in Canton. USA in 1986. it was the first such conference organized in Europe. It brought together 70 scientists from 11 countries. Organizers were Professor A. Cambini. University of Pisa. Professor E. Castagnoli. Bocconi University. Milano. Professor L. Martein. University of Pisa. Professor P. Mazzoleni. University of Verona and Professor S. Schaible. University of California. Riverside.

Editors and Affiliations

  • Department of Statistics and Applied Mathematics, University of Pisa, Pisa, Italy

    Alberto Cambini, Laura Martein

  • Institute of Quantitative Methods, Bocconi University, Milano, Italy

    Erio Castagnoli

  • Institute of Mathematics, University of Verona, Verona, Italy

    Piera Mazzoleni

  • Graduate School of Management, University of California, Riverside, USA

    Siegfried Schaible

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