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Global error bounds for the extended vertical LCP

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Abstract

A new necessary and sufficient condition for the row \(\mathcal{W}\) -property is given. By using this new condition and a special row rearrangement, we provide two global error bounds for the extended vertical linear complementarity problem under the row \(\mathcal{W}\) -property, which extend the error bounds given in Chen and Xiang (Math. Program. 106:513–525, 2006) and Mathias and Pang (Linear Algebra Appl. 132:123–136, 1990) for the P-matrix linear complementarity problem, respectively. We show that one of the new error bounds is sharper than the other, and it can be computed easily for some special class of the row \(\mathcal{W}\) -property block matrix. Numerical examples are given to illustrate the error bounds.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Hirosaki University, Hirosaki, 036-8561, Japan

    Chao Zhang & Xiaojun Chen

  2. Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Naihua Xiu

Authors
  1. Chao Zhang
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  2. Xiaojun Chen
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  3. Naihua Xiu
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Correspondence to Xiaojun Chen.

Additional information

The work was in part supported by a Grant-in-Aid from Japan Society for the Promotion of Science, and the National Natural Science Foundation of China (10671010).

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Zhang, C., Chen, X. & Xiu, N. Global error bounds for the extended vertical LCP. Comput Optim Appl 42, 335–352 (2009). https://doi.org/10.1007/s10589-007-9134-9

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  • DOI: https://doi.org/10.1007/s10589-007-9134-9

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