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A sign-based linear method for horizontal linear complementarity problems

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Abstract

For the horizontal linear complementarity problem, we establish a linear method based on the sign patterns of the solution of the equivalent modulus equation under the assumption of strict complementarity. The new method is equivalent to solving two linear equations, avoiding parameters selection, so it is more convenient and practical. Numerical examples show that the new method is superior to the previous modulus-based matrix splitting iterative method, two-step modulus-based matrix splitting iterative method and modulus-based nonsmooth Newton’s method in computing efficiency. The new method can be used as a solution scheme to the horizontal complementarity problem of large sparse matrices.

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Funding

The work was supported by the Natural Science Foundation of Liaoning Province (No. 20170540323) and Central University Basic Scientific Research Business Expenses Special Funds (N2005013).

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  1. Department of Mathematics, College of Sciences, Northeastern University, Shenyang, China

    Xin-Hui Shao, Zhe Wang & Hai-Long Shen

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  1. Xin-Hui Shao
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  2. Zhe Wang
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Correspondence to Xin-Hui Shao.

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Shao, XH., Wang, Z. & Shen, HL. A sign-based linear method for horizontal linear complementarity problems. Numer Algor 91, 1165–1181 (2022). https://doi.org/10.1007/s11075-022-01296-w

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