Set-convergence of convex sets and stability in vector optimization
Enrico Miglierina · RePEc: Research Papers in Economics · 2002
This work establishes the lower convergence of the set of minimal points of An to the set of minimal points of A, whenever An is a sequence of convex subsets of an euclidean space satisfying the dominance property and converging to A. Using this result and introducing a property for a function f that guarantees the convergence of the image f(An) to f(A) when An converges to A, we obtain some stability results in the decision space for a class of suitable perturbations of the feasible region of a vector optimization problem.