Abstract

In this paper we present a generalization of the predictor corrector method of linear programming problem to semidefinite linear programming problem. We consider a direction which, we show, belongs to a family of directions presented by Kojima, Shindoh 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( ffl t 0 )j p n) iterations of the predictor corrector method, the complementary slackness violation can be reduced to less than or equal to ffl ? 0. We also analyze a modified corrector direction in which the linear system to be solved differs from that of the predictor in only the right hand side, and obtain a similar bound. We then use this modified corrector step in an implementable method which is shown to take a total of O(jlog( ffl t 0 )j p nlog(n)) predictor and corrector steps. Key words: Linear programming, Semidefinite programming, Interior point methods, Path following, ...

Citations