Extension of a polynomial time mehrotra-type predictor-corrector safeguarded algorithm to monotone linear complementarity problems

Abstract

Mehrotra-type predictor-corrector algorithms are the basis of interior point methods software packages. Salahi et al. in their recent work have shown a feasible version of a variation of Mehrotra's second order algorithm for linear optimization may be forced to make many small steps that motivated them to introduce certain safeguards, what allowed them to prove polynomial iteration complexity while keeping its practice efficiency. In this paper, we extend their algorithm to monotone linear complementarity problems. Our algorithm is different from their method in the way of updating the barrier parameter and the complexity analysis, and we also show that the polynomial complexity of our algorithm is O(n2 log (x0)T s 0/ε). © 2008 Springer-Verlag Berlin Heidelberg.