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: 181

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 .

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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,

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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

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

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