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
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.