ON DIRECTIONAL METRIC SUBREGULARITY AND SECOND-ORDER OPTIMALITY CONDITIONS FOR A CLASS OF NONSMOOTH MATHEMATICAL PROGRAMS

We study infinite dimensional optimization problems where the constraint mapping is given as the sum of a smooth function and a generalized polyhedral multifunction, e. g., the normal cone mapping of a convex polyhedral set. By using advanced techniques of variational analysis we obtain first-order and second-order characterizations, both necessary and sufficient, for directional metric subregularity of the constraint mapping. These results are used to obtain second-order optimality conditions for the optimization problem.