A TWO-STEP PRIMAL-DUAL INTERIOR POINT METHOD FOR NONLINEAR SEMIDEFINITE PROGRAMMING PROBLEMS AND ITS SUPERLINEAR CONVERGENCE

Abstract

In this paper, we propose a primal-dual interior point method for nonlinear semidefinite programming problems and show its superlinear convergence. This method is based on generalized shifted barrier Karush-Kuhn-Tucker (KKT) conditions, which include barrier KKT conditions and shifted barrier KKT conditions as a special case. This method solves two Newton equations in a single iteration to guarantee superlinear convergence. We replace the coefficient matrix of the second Newton equation with that of the first to reduce the computational time of the single iteration. We show that the superlinear convergence of the proposed method with the replacement under the usual assumptions.