Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2013-004 (July 22, 2013)

A differentiable merit function for the shifted perturbed KKT conditions of the nonlinear semidefinite programming
by Yuya Yamakawa and Nobuo Yamashita

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In this paper we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems, which is based on the shifted perturbed KKT conditions. The main task of the interior point method is to get a point approximately satisfying the shifted perturbed KKT conditions. We first propose a differentiable merit function whose stationary points always satisfy the conditions. The function is an extension of that proposed by Forsgren and Gill for the nonlinear programming problem. Then, we develop a Newton type method that finds a stationary point of the merit function. We show the global convergence of the proposed Newton type method under some mild conditions. Finally, we report some numerical results which show that the proposed method is competitive to the existing primal-dual interior point method based on the perturbed KKT conditions.