Local-global efficiency properties for multiobjective max-min programming

Authors

  • Ştefan Ţigan University of Medicine and Pharmacy “Iuliu Hatieganu”, Cluj-Napoca, Romania
  • Ioan M. Stancu-Minasian “Gheorghe Mihoc–Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Bucharest, Romania

DOI:

https://doi.org/10.33993/jnaat332-785

Keywords:

vector programming, pseudomonotonic programming, max-min efficiency, proper max-min efficiency
Abstract views: 183

Abstract

The purpose of this paper is to give sufficient conditions of generalized concavity and convexity type for a local (weakly) max-min efficient solution to be a global (weakly) max-min efficient solution for an vector maxmin programming problem.   In the particular case of the vector max-min pseudomonotonic programming problem{}, we derive some characterizations properties of max-min efficient and properly max-min efficient solutions .

Downloads

Download data is not yet available.

References

Geoffrion, A. M., Proper efficiency and the theory of vector maximization, J. Math. Anal. Appl., 22, no. 3, pp. 618-630, 1968, https://doi.org/10.1016/0022-247X(68)90201-1. DOI: https://doi.org/10.1016/0022-247X(68)90201-1

Luc, D. T. and Schaible, S., Efficiency and generalized concavity, J. Optim. Theory Appl., 94, no. 1, pp. 147-153, 1997, https://doi.org/10.1023/A:1022663804177. DOI: https://doi.org/10.1023/A:1022663804177

Ruiz-Canales, P. and Rufian-Lizana, A., A characterization of weakly efficient points, Math. Progr., 68, pp. 205-212, 1995, https://doi.org/10.1007/BF01585765. DOI: https://doi.org/10.1007/BF01585765

Stancu-Minasian, I. M., Metode de rezolvare a problemelor de programare fracţionară, Editura Academiei Române, Bucureşti, 1992 (in Romanian).

Tigan, S. and Stancu-Minasian, I. M., Efficiency properties for stochastic multiobjective programming, In Proceedings of "Tiberiu Popoviciu" Itinerant Seminar of Functional Equations, Approximation and Convexity, Cluj-Napoca, 2002, E. Popoviciu (eds.), pp. 271-290, Editura SRIMA, Cluj-Napoca, 2002.

Tigan, S. and Stancu-Minasian, I. M., Efficiency and generalized concavity for multiobjective set-valued programming, Rev. Anal. Numér. Théor. Approx., 32, no. 2, pp. 235-242, 2003, http://ictp.acad.ro/jnaat/journal/article/view/2003-vol32-no2-art12

Weber R., Pseudomonotonic Multiobjective Programming. Discussion Paper, Institute of Operations Research, Department of Economics, University of Saarland, Saarbruecken,

Downloads

Published

2004-08-01

How to Cite

Ţigan, Ştefan, & Stancu-Minasian, I. M. (2004). Local-global efficiency properties for multiobjective max-min programming. Rev. Anal. Numér. Théor. Approx., 33(2), 251–257. https://doi.org/10.33993/jnaat332-785

Issue

Vol. 33 No. 2 (2004)

Section

Articles

License

Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.