An inexact non-interior continuation method for semidefinite programming: convergence analysis and numerical results

Abstract

In this paper, an inexact non-interior continuation method is proposed for semidefinite Programs. By a matrix mapping, the primal-dual optimal condition can be inverted into a smoothed nonlinear system of equations. A linear system of equations with residual vector is eventually driven by solving the smoothed nonlinear system of equations and finally solved by the conjugate residual method. The global and locally superlinear convergence are verified. Numerical results and comparisons indicate that the proposed methods are very promising and comparable to several interior-point and other exact non-interior continuation methods.