ON OPTIMALITY CONDITIONS FOR ABSTRACT CONVEX VECTOR OPTIMIZATION PROBLEMS

- Journal title : Journal of the Korean Mathematical Society
- Volume 44, Issue 4, 2007, pp.971-985
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2007.44.4.971

Title & Authors

ON OPTIMALITY CONDITIONS FOR ABSTRACT CONVEX VECTOR OPTIMIZATION PROBLEMS

Lee, Gue-Myung; Lee, Kwang-Baik;

Lee, Gue-Myung; Lee, Kwang-Baik;

Abstract

A sequential optimality condition characterizing the efficient solution without any constraint qualification for an abstract convex vector optimization problem is given in sequential forms using subdifferentials and -subdifferentials. Another sequential condition involving only the subdifferentials, but at nearby points to the efficient solution for constraints, is also derived. Moreover, we present a proposition with a sufficient condition for an efficient solution to be properly efficient, which are a generalization of the well-known Isermann result for a linear vector optimization problem. An example is given to illustrate the significance of our main results. Also, we give an example showing that the proper efficiency may not imply certain closeness assumption.

Keywords

convex vector optimization problem;optimality conditions;efficient solution;properly efficient solution;convex function;

Language

English

Cited by

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