Convergence and Approximation of Optimization Problems

Abstract

In this paper we consider a optimization problem (OP) and study the convergence and approximation of optimal values and optimal solutions to changes in the cost function and the set of feasible solutions. By a general OP we mean that the cost function and the constraints are defined on a Hausdorff topological space. First we obtain convergence results for a OP, and then we present an application of these results on the approximation of the optimal value and the optimal solutions for the so-called capacity problem in metric spaces.