Abstract
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.
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