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Superlinear Noninterior One-Step Continuation Method for Monotone LCP in the Absence of Strict Complementarity

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  • B. Chen
  • N. Xiu

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).

Suggested Citation

  • B. Chen & N. Xiu, 2001. "Superlinear Noninterior One-Step Continuation Method for Monotone LCP in the Absence of Strict Complementarity," Journal of Optimization Theory and Applications, Springer, vol. 108(2), pages 317-332, February.
    • Handle: RePEc:spr:joptap:v:108:y:2001:i:2:d:10.1023_a:1026486217222
    DOI: 10.1023/A:1026486217222
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    References listed on IDEAS

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    1. James V. Burke & Song Xu, 1998. "The Global Linear Convergence of a Noninterior Path-Following Algorithm for Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 719-734, August.
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