A DIFFERENTIABLE MERIT FUNCTION FOR SHIFTED PERTURBED KARUSH-KUHN-TUCKER CONDITIONS OF THE NONLINEAR SEMIDEFINITE PROGRAMMING

作者：Yamakawa Yuya^*; Yamashita Nobuo

来源：Pacific Journal of Optimization, 2015, 11(3): 557-579.

• merit function
• Newton-type method
• nonlinear semidefinite programming
• primal-dual interior point method
• shifted perturbed Karush-Kuhn-Tucker conditions

In this paper we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems, which is based on shifted perturbed Karush-Kuhn-Tucker (KKT) conditions. The main task addressed by the interior point method is to obtain a point that approximately satisfies shifted perturbed KKT conditions. First, we propose a differentiable merit function whose stationary points always satisfy the conditions. This function is an extension of the one proposed by Forsgren and Gill for nonlinear programming problems. Next, 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 performance of the proposed method is comparable to the existing primal-dual interior point method based on perturbed KKT conditions.

• 出版日期2015-7