Pointwise well-posedness and scalarization in set optimization

Abstract

In this paper, some notions of pointwise well-posedness for set optimization problems are introduced. Some relationships among these notions are established. Using a new nonlinear scalarization function, pointwise well-posed set optimization problems are characterized by means of a family of Tykhonov well-posed scalar optimization problems. Also, three classes of well-posed set optimization problems are identified.

Continuity of solutions mappings of parametric set optimization problems

“…Since then, the optimality, convexity, well-posedness, existence, duality, scalarization and algorithms in set optimization problems have been studied under different kinds of set order relations; see, e.g. [1,3,4,5,7,8,9,10,11,13,14,16,24,25,29] and the references therein.…”

Pointwise well-posedness and scalarization of optimization problems for locally convex cone-valued functions

“…Since then, various notions of well-posedness were introduced and studied for scalar optimization problems (see [4], [6]). In the last decades, some extensions of this concept to the vector optimization problems were appeared (see [2,3], [5], [8], [12,13]) and recently we have some extensions of that to the set optimization problems (see [7], [10,11], [23]). Our aim in the present work is twofold.…”