On upper semicontinuity of global minima in constrained optimization problems

This paper studies stability properties of solutions for optimization problems subject to perturbations in constraints. For problems formulated in a complete metric space sufficient conditions for topological upper semicontinuity of the solution multifunction are derived without any compactness assumptions. When the feasible solution set is additionally assumed to be compact these conditions reduce to that of Berge (“Topological Spaces,” Macmillan Co., New York, 1963), and in that case they turn out to be also necessary.