CONVEXITY AND GLOBAL WELL-POSEDNESS IN SET-OPTIMIZATION

Abstract

Well-posedness for vector optimization problems has been extensively studied. More recently, some attempts to extend thee results to set-valued optimization have been proposed, mainly applying some scalarization. In this paper we propose a new definition of global well-posedness for set-optimization problems. Using an embedding technique proposed by Kuroiwa and Nuriya (2006), we prove well-posedness property of a class of generalized convex set-valued maps.