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Perturbation analysis of nonlinear semidefinite programming under Jacobian uniqueness conditions

Ziran Yin(yinziran***at***mail.dlut.edu.cn)
Liwei Zhang(lwzhang***at***dlut.edu.cn)

Abstract: We consider the stability of a class of parameterized nonlinear semidefinite programming problems whose objective function and constraint mapping all have second partial derivatives only with respect to the decision variable which are jointly continuous. 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 perturbed problem also satisfies the Jacobian uniqueness conditions at some feasible point.

Keywords: nonlinear semidefinite programming; Jacobian uniqueness conditions; KKT system; implicit function theorem.

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )


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Entry Submitted: 09/11/2017
Entry Accepted: 09/12/2017
Entry Last Modified: 09/11/2017

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