Advertisement

Reciprocity in Optimization and Efficiency in the Bicriteria Problem: A Unified Approach

  • Alberto Cambini
  • Laura Martein
Conference paper
Part of the Operations Research Proceedings book series (ORP, volume 1990)

Abstract

In this paper we will suggest a general framework within which reciprocity in scalar optimization and efficiency for a bicriteria problem can be studied, with the aim of obtaining a unified approach in order to link together some concepts and properties which are appeared in the literature in different fields and problems [3, 6, 7, 11, 13, 14].

The followed approach will allow us to analyze efficiency, reciprocity and related concepts all together in order to study the connections among them and, at the same time, to establish, in a simple way, old and new results and also wide classes of problems for which reciprocity and binding properties hold.

Keywords

Binding Property Portfolio Selection Parametric Problem Vector Optimization Problem Fractional Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    H. Avriel, W. E. Diewert, S. Schaible, I. Zang, “Generalized Concavity” Plenum Press. New York and London (1988)Google Scholar
  2. [2]
    H. P. Benson, “Vector maximization with two objective functions”. Journal of Optimization Theory and Applications, vol. 28, pp. 253–257, (1979)CrossRefGoogle Scholar
  3. [3]
    M.B. Borgheaani, “Considerazioni sulla reciprocità nei problemi di ottimo” Rivista di Matematica per le Scienze Economiche e Sociali; Fascicolo n. 2, (1986)Google Scholar
  4. [4]
    A. Cambini, L. Martein, “The linear fractional and the bicriteria linear fractional problem”, in Generalized Concavity, Fractional Programming and Economic Applications, edited by Cambini A., Castagnoli E., Martein L., Mazzoleni P., Schaible S., Springer-Verlag, Berlin (1990)Google Scholar
  5. [5]
    B. U. Choo, D. R. Atkins, “Bicriteria linear fractional programming”, Journal of Optimization Theory and Application, vol.36, pp. 203–220, (1982)CrossRefGoogle Scholar
  6. [6]
    P. Ftvati, M. Pappalardo, “On the Reciprocal Vector Optimization Problems”. Journal of Optimization Theory and Applications, vol. 47, pp. 181–193, (1985)CrossRefGoogle Scholar
  7. [7]
    N. D. Kazarinoff, “Geometric inequalities” New Math. Library, (1961)Google Scholar
  8. [8]
    P. Madden, “Concavitv and optimization in microeconomics”. Basil Blackwell (1986)Google Scholar
  9. [9]
    H.W. Markowitz, “Portfolio selection: efficient diversification of investements”. J. Wiley & Sons. (1959)Google Scholar
  10. [10]
    A. Marchi, “A Sequential Method for a Bicriteria Problem arising in Portfolio Selection Theory”. Department of Statistics and Applied Mathematics, University of Pisa, paper n. 30, (1990)Google Scholar
  11. [11]
    L. Martein, “On the bicriteria maximization problem” in Generalized Concavity, Fractional Programming and Economic Applications, edited by Cambini A., Castagnoli E., Martein L., Mazzoleni P., Schaible S., Springer-Verlag, Berlin, (1990)Google Scholar
  12. [12]
    L. Martein, S. Schaible, “On solving a linear program with a quadratic constraint”. Rivista di Matematica per le Scienze Economiche e Sociali, Fascicolo 1–2, pp. 75–90, (1988)Google Scholar
  13. [13]
    S. Schaible, “Bicriteria auasiconcave programs”. Cahiers du C.E.R.O.,vol.25, pp.93–101 (1983)Google Scholar
  14. [14]
    M. Volpato, “Studi e modelli di ricerca operativa”. UTET, Torino (1971)Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1992

Authors and Affiliations

  • Alberto Cambini
    • 1
  • Laura Martein
    • 1
  1. 1.PisaItaly

Personalised recommendations