Search directions and convergence analysis of some infeasibnle path-following methods for the monoton semi-definite lcp^∗

^∗This research is supported by National Science Foundation Grant CCR-9311621

Abstract

We consider a family of primal/primal-dual/dual search directions for the monotone LCP over the space of n× nsymmetric block-diagonal matrices. We consider twio infea-sible predictor-corrector path-following methods using these search directions, with the predictor and corrector steps used either in series (similar to the Mizuno-Todd-Ye method) or in parallel (similar to Mizuno et al./McShane's method). The methods attaijn global linear convergence with a convergence ratio which, depending on the quality of the starting iterate, ranges from .Our analysis is fairly compact and parallels that for the LP and LCP cases

Keywords:

• Search Directions
• Convergence
• Path-Following
• Monotone Semi-Definite LCP

^∗This research is supported by National Science Foundation Grant CCR-9311621

^∗This research is supported by National Science Foundation Grant CCR-9311621

Notes

^∗This research is supported by National Science Foundation Grant CCR-9311621