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Constructions of complementarity functions and merit functions for circular cone complementarity problem

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Abstract

In this paper, we consider complementarity problem associated with circular cone, which is a type of nonsymmetric cone complementarity problem. The main purpose of this paper is to show the readers how to construct complementarity functions for such nonsymmetric cone complementarity problem, and propose a few merit functions for solving such a complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also show that these merit functions provide an error bound for the circular cone complementarity problem. These results ensure that the sequence generated by descent methods has at least one accumulation point, and build up a theoretical basis for designing the merit function method for solving circular cone complementarity problem.

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Acknowledgments

Xin-He Miao work is supported by National Young Natural Science Foundation (No. 11101302 and No. 61002027) and National Natural Science Foundation of China (No. 11471241). Jein-Shan Chen work is supported by Ministry of Science and Technology, Taiwan.

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Authors and Affiliations

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

    Xin-He Miao, Shengjuan Guo & Nuo Qi

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

    Jein-Shan Chen

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  1. Xin-He Miao
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  2. Shengjuan Guo
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  3. Nuo Qi
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  4. Jein-Shan Chen
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Correspondence to Jein-Shan Chen.

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Miao, XH., Guo, S., Qi, N. et al. Constructions of complementarity functions and merit functions for circular cone complementarity problem. Comput Optim Appl 63, 495–522 (2016). https://doi.org/10.1007/s10589-015-9781-1

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