Perturbation analysis of nonlinear semidefinite programming under Jacobian uniqueness conditions

摘要

This paper extends a stability results of nonlinear programming problems by Robinson (Math Program 7:1-16, 1974) to nonlinear semidefinite programming problems. We apply an implicit function theorem to a reformulated Karush-Kuhn-Tucker system, while the Robinson's work is directly related to the conventional Karush-Kuhn-Tucker system. We show that when the Karush-Kuhn-Tucker condition, constraint nondegeneracy condition, strict complementary condition and second order sufficient condition are satisfied at a feasible point of the original problem, the perturbed problem also satisfies these conditions at some stationary point.