Scalarization and Well-posedness for Set Optimization using Coradiant Sets

Abstract

The aim of this paper is to study scalarization and well-posedness for a set-valued optimization problem with order relations induced by a coradiant set. We introduce the notions of the set criterion solution for this problem and obtain some characterizations for these solutions by means of a nonlinear scalarization function. The scalarization funciton is a generalization of the scalarization function introduced by Khoshkhabar-amiranloo and Khorram. Moveover, we define the pointwise notions of $LP$ well-posedness, strong $DH$-well-posedness and strongly $B$-well-posedness for the set optimization problem and characterize these properties through some scalar optimization problems based on the generalized nonlinear scalarization function, respectively.