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A Smoothing-Type Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties

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Abstract

In this paper, we construct an augmented system of the standard monotone linear complementarity problem (LCP), and establish the relations between the augmented system and the LCP. We present a smoothing-type algorithm for solving the augmented system. The algorithm is shown to be globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, if the LCP has a solution, then the algorithm either generates a maximal complementary solution of the LCP or detects correctly solvability of the LCP, and in the latter case, an existing smoothing-type algorithm can be directly applied to solve the LCP without any additional assumption and it generates a maximal complementary solution of the LCP; and that if the LCP is infeasible, then the algorithm detect correctly infeasibility of the LCP. To the best of our knowledge, such properties have not appeared in the existing literature for smoothing-type algorithms.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, People’s Republic of China

    Zheng-Hai Huang & Wei-Zhe Gu

Authors
  1. Zheng-Hai Huang
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  2. Wei-Zhe Gu
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Correspondence to Zheng-Hai Huang.

Additional information

This work was partially supported by the National Natural Science Foundation of China (Grant No. 10571134), the Natural Science Foundation of Tianjin (Grant No. 07JCYBJC05200), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

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Huang, ZH., Gu, WZ. A Smoothing-Type Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties. Appl Math Optim 57, 17–29 (2008). https://doi.org/10.1007/s00245-007-9004-y

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