Abstract
We propose a noninterior continuation method for the monotone linear complementarity problem (LCP) by modifying the Burke–Xu framework of the noninterior predictor-corrector path-following method (Refs. 1–2). The new method solves one system of linear equations and carries out only one line search at each iteration. It is shown to converge to the LCP solution globally linearly and locally superlinearly without the assumption of strict complementarity at the solution. Our analysis of the continuation method is based on a broader class of the smooth functions introduced by Chen and Mangasarian (Ref. 3).
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