Second-order Optimality Conditions for Mathematical Program with Semidefinite Cone Complementarity Constraints and Applications

摘要

This paper is concerned with second-order optimality conditions for the mathematical program with semidefinite cone complementarity constraints. To achieve this goal, we first provide an exact characterization on the second-order tangent set to the semidefinite cone complementarity set in terms of the second-order directional derivative of the projection operator onto the semidefinite cone complementarity set, and then use the second-order tangent set to the semidefinite cone complementarity set to derive second-order necessary and sufficient conditions for the mathematical program with semidefinite cone complementarity constraints under suitable subregularity constraint qualifications. The obtained second-order necessary optimality condition is also illustrated via the mathematical program with semidefinite cone complementarity constraints reformulation of semidefinite rank regularized problem.

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