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We consider the stability of a class of parameterized conic programming problems which are more general than $C^2$-smooth parameterization. We show that when the Karush-Kuhn-Tucker (KKT) condition, the constraint nondegeneracy condition, the strict complementary condition and the second order sufficient condition (named as Jacobian uniqueness conditions here) are satisfied at a feasible point of the original problem, the Jacobian uniqueness conditions of the perturbed problem also hold at some feasible point.

Perturbation analysis of a class of conic programming problems under Jacobian uniqueness conditions