Levitin-Polyak well-posedness for generalized semi-infinite multiobjective programming problems

Abstract

Abstract In this paper, we introduce a notion of Levitin-Polyak well-posedness for generalized semi-infinite multiobjective programming problems in terms of weakly efficient solutions. We obtain some metric characterizations of Levitin-Polyak well-posedness for this problem. We derive the relations between the Levitin-Polyak well-posedness and the upper semi-continuity of approximate solution maps for generalized semi-infinite multiobjective programming problems. Examples are given to illustrate our main results.

Keywords

• generalized semi-infinite multiobjective programming problem
• Levitin-Polyak well-posedness
• approximate solution map
• metric characterization
• upper semi-continuity