Convergence and approximation of optimization problems

In this paper we consider a general 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 general 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 general capacity problem in metric spaces.