Pointwise Well-Posedness and Scalarization for Set Optimization Problems with a Partial Order Relation

Pakkapon Preechasilp, Rabian Wangkeeree

Abstract

The present paper aims to obtain some relation among three kinds of pointwise well-posedness for set optimization problems with $ \preu $ order. By using a nonlinear scalarization function, we establish some relations between the three kinds of pointwise well-posedness for set optimization problems and the well-posedness of scalar optimization problems, respectively. Some global well-posedness notions are studied. Finally, we discuss the results to robust vector optimization problems.