Convergence Analysisof Some Infeasible Path - following Methodsfor the Monotone Semi - Definite Lcp 1
نویسنده
چکیده
We consider a family of primal/primal-dual/dual search directions for the monotone LCP over the space of n n symmetric block-diagonal matrices. We consider two infeasible 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 attain global linear convergence with a convergence ratio which, depending on the quality of the starting iterate, ranges from 1 ? O(p n) ?1 to 1 ? O(n) ?1. Our analysis is fairly simple and parallels that for the LP and LCP cases.
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