Stability kernel of vector optimization problems under perturbations of criterion functions

Abstract

The article is devoted to the study of the influence of uncertainty in initial data on the solutions of optimization multicriterial problems. In the optimization problems, including problems with vector criterion, small perturbations in initial data can result in solutions strongly different from the true ones. The results of the conducted researches allow us to extend the known class of vector optimization problems, stable with respect to input data perturbations in vector criterion. We are talking about stability in the sense of Hausdorff lower semicontinuity for point-set mapping that characterizes the dependence of the set of optimal solutions on the input data of the vector optimization problem. The conditions of stability against input data perturbations in vector criterion for the problem of finding Pareto optimal solutions with continuous partial criterion functions and feasible set of arbitrary structure are obtained by studying the sets of points that are stable belonging and stable not belonging to the Pareto set.