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Smoothing functions and algorithm for nonsymmetric circular cone complementarity problems

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Abstract

There has been much interest in studying symmetric cone complementarity problems. In this paper, we study the circular cone complementarity problem (denoted by CCCP) which is a type of nonsymmetric cone complementarity problem. We first construct two smoothing functions for the CCCP and show that they are all coercive and strong semismooth. Then we propose a smoothing algorithm to solve the CCCP. The proposed algorithm generates an infinite sequence such that the value of the merit function converges to zero. Moreover, we show that the iteration sequence must be bounded if the solution set of the CCCP is nonempty and bounded. At last, we prove that the proposed algorithm has local superlinear or quadratical convergence under some assumptions which are much weaker than Jacobian nonsingularity assumption. Some numerical results are reported which demonstrate that our algorithm is very effective for solving CCCPs.

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Acknowledgments

We are very grateful to the referees for their valuable comments on the paper, which have considerably improved the paper.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Xinyang Normal University, 464000, Xinyang, P.R. China

    Jingyong Tang & Yuefen Chen

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  1. Jingyong Tang
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  2. Yuefen Chen
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Corresponding author

Correspondence to Jingyong Tang.

Additional information

This work was supported by the National Natural Science Foundation of China (11601466), Natural Science Foundation of Henan Province (202300410343) and the Training Plan of Young Key Teachers in Universities of Henan Province (2018GGJS096).

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Tang, J., Chen, Y. Smoothing functions and algorithm for nonsymmetric circular cone complementarity problems. Appl Math 67, 209–231 (2022). https://doi.org/10.21136/AM.2021.0129-20

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  • DOI: https://doi.org/10.21136/AM.2021.0129-20

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