Well-posedness for set optimization problems

Generic Well-posedness for Perturbed Optimization Problems in Banach Spaces

Let X be a Banach space and Z a relatively weakly compact subset of X. Let J : Z → R be a upper semicontinuous function bounded from above and p ≥ 1. This paper is concerned with the perturbed optimization problem of finding z0 ∈ Z such that ‖x− z0‖ + J(z0) = supz∈Z{‖x− z‖p + J(z)}, which is denoted by maxJ(x, Z). We prove in the present paper that if X is Kadec w.r.t. Z, then the set of all x ...

Well-posedness for Hyperbolic Problems

Tykhonov Well-Posedness for Quasi-Equilibrium Problems

We consider an extension of the notion of Tykhonov well-posedness for perturbed vector quasi-equilibrium problems. We establish some necessary and sufficient conditions for verifying these well-posedness properties. As for applications of our results, the Tykhonov well-posedness of vector variational-like inequalities and vector optimization problems are established

Well-posedness for Lexicographic Vector Equilibrium Problems

We consider lexicographic vector equilibrium problems in metric spaces. Sufficient conditions for a family of such problems to be (uniquely) well-posed at the reference point are established. As an application, we derive several results on well-posedness for a class of variational inequalities.

Generic Well-posedness in Minimization Problems

The goal of this paper is to provide an overview of results concerning, roughly speaking, the following issue: given a (topologized) class of minimum problems, “how many” of them are well-posed? We will consider several ways to define the concept of “how many,” and also several types of well-posedness concepts. We will concentrate our attention on results related to uniform convergence on bound...