Weakly-Efficient Solutions Of Limiting Multicriteria Optimization Problems

Abstract

This paper concerns the connection among different sets of multicriteria optimization problem solutions. For the family of bicriteria optimization problems the limiting properties of the sets of weakly-efficient solutions are determined.

Résumé

Dans cette article on étudie la liason entre des ensembles differentes de solutions des problèmes multicritériales d’optimisation. Pour la famille de problèmes d’optimisation bicritériales, on étudie des proprietés limités des ensembles de solutions peu-effectives.

Key words::

• Multicriteria optimization
• efficient
• weakly-efficient
• proper efficient solutions

Additional information

Notes on contributors

M. E. Salukvadze

Mindia Salukvadze was born in Tbilisi, Georgia, USSR on 3 May, 1933. He graduated from the physics department of Tbilisi State University in 1955. He received degrees of candidate and doctor of technical sciences in technical cybernetics from the Institute of Control Problems, Moscow, in 1963 and 1974, respectively. He is Professor (1980) and correspondent-member of the Georgian Academy of Sciences (1983). He is Laureate of the Georgian state prize (1979). From 1958 up to today he is at the Institute of Control Systems of the Georgian Academy of Sciences, Tbilisi. From 1982, he has been the Director. He is the author of five monographs. His research interests are in control theory, multicriteria optimization and game theory.

A. L. Topchishvili

Alexander Topchishvili was born in Tbilisi, Georgia, USSR on 17 April, 1958. He graduated from the mathematical-mechanics department of Leningrad State University in 1980 and received his degree of candidate of technical sciences in engineering systems control from Georgian Technical University, Tbilisi, in 1987. From 1980 up to today, he is at the Institute of Control Systems of the Georgian Academy of Sciences, Tbilisi, Georgia. Currently he is a Leading Researcher in the Department of Optimization Methods. His research interests are in continuous and discrete mathematical programming, multicriteria optimization, control theory and it’s application to real-world processes.