On the existence and the stability of solutions in nonconvex vector optimization

TL;DR

This paper investigates the existence and stability of solutions in nonconvex vector optimization problems, introducing new conditions using asymptotic cones and functions, with applications to robustly quasiconvex problems.

Contribution

It establishes conditions for solution existence and stability in nonconvex vector optimization using asymptotic analysis, extending previous results to unbounded and perturbed problems.

Findings

Conditions for weak Pareto solutions and weak sharp minima at infinity.

Solution stability results under linear perturbations.

Applications to robustly quasiconvex vector optimization.

Abstract

The paper is devoted to the existence of weak Pareto solutions and the weak sharp minima at infinity property for a general class of constrained nonconvex vector optimization problems with unbounded constraint set via asymptotic cones and generalized asymptotic functions. Then we show that these conditions are useful for studying the solution stability of nonconvex vector optimization problems with linear perturbation. We also provide some applications for a subclass of robustly quasiconvex vector optimization problems.