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An inexact alternating direction method of multipliers for the solution of linear complementarity problems arising from free boundary problems

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Abstract

A large number of free boundary problems can be formulated as linear-complementarity problems. In this paper, we propose an inexact alternating direction method of multipliers for solving linear complementarity problem arising from free boundary problems by using the special structure of these problems. The convergence of our proposed method is proved. Numerical results show that the proposed method is feasible and effective, and it is significantly faster than modified alternating direction implicit algorithm and many other methods, especially when dimension of the problem being solved is large.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Jian-Jun Zhang, Jian-Li Zhang & Wan-Zhou Ye

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  1. Jian-Jun Zhang
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  2. Jian-Li Zhang
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  3. Wan-Zhou Ye
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Correspondence to Jian-Jun Zhang.

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Zhang, JJ., Zhang, JL. & Ye, WZ. An inexact alternating direction method of multipliers for the solution of linear complementarity problems arising from free boundary problems. Numer Algor 78, 895–910 (2018). https://doi.org/10.1007/s11075-017-0405-y

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  • DOI: https://doi.org/10.1007/s11075-017-0405-y

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