Abstract:

The data of problem are often perturbed in real life. We often calculate the solution of a perturbed problem to approximate the original problem solution. Therefore, the stability of the solution set of the original problem is an important issue. In this paper, we consider a class of non-convex vector optimization problems with two mapping differences. By taking advantage of appropriate convergence and convexity of the two mappings, the stability results of the nonconvex vector optimization problem is obtained, when the approximate problem data converge to the original problem data in the sense of Painlevé-Kuratowski's convergence.

Key words: non-convex optimization, Painlevé-Kuratowski convergence, stability, properly quasi $C$-concave, $C$-convex