A Predictor Corrector Method for Semi - de nite

In this paper we present a generalization of the predictor corrector method of linear programming problem to semideenite linear programming problem. We consider a direction which, we show, belongs to a family of directions presented by Kojima, Shin-doh and Hara, and, one of the directions analyzed by Monteiro. We show that starting with the initial complementary slackness violation of t 0 , in O(jlog(t0)j p n) iterations of the predictor corrector method, the complementary slackness violation can be reduced to less than or equal to > 0. We also analyze a modiied corrector direction in which the linear system to be solved diiers from that of the predictor in only the right hand side, and obtain a similar bound. We then use this modiied corrector step in an implementable method which is shown to take a total of O(jlog(t0)j p nlog(n)) predictor and corrector steps.