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On merit functions for p-order cone complementarity problem

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Abstract

Merit function approach is a popular method to deal with complementarity problems, in which the complementarity problem is recast as an unconstrained minimization via merit function or complementarity function. In this paper, for the complementarity problem associated with p-order cone, which is a type of nonsymmetric cone complementarity problem, we show the readers how to construct merit functions for solving p-order cone complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also assert that these merit functions provide an error bound for the p-order cone complementarity problem. These results build up a theoretical basis for the merit method for solving p-order cone complementarity problem.

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Authors and Affiliations

  1. Department of Mathematics, Tianjin University, Tianjin, 300072, China

    Xin-He Miao

  2. Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan

    Yu-Lin Chang & Jein-Shan Chen

Authors
  1. Xin-He Miao
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  2. Yu-Lin Chang
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  3. Jein-Shan Chen
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Corresponding author

Correspondence to Jein-Shan Chen.

Additional information

X.-H. Miao: The author’s work is supported by National Natural Science Foundation of China (No. 11471241).

J.-S. Chen: The author’s work is supported by Ministry of Science and Technology, Taiwan.

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Miao, XH., Chang, YL. & Chen, JS. On merit functions for p-order cone complementarity problem. Comput Optim Appl 67, 155–173 (2017). https://doi.org/10.1007/s10589-016-9889-y

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  • DOI: https://doi.org/10.1007/s10589-016-9889-y

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