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A Semidefinite Relaxation Method for Linear and Nonlinear Complementarity Problems with Polynomials

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Abstract

This paper considers semidefinite relaxation for linear and nonlinear complementarity problems. For some particular copositive matrices and tensors, the existence of a solution for the corresponding complementarity problems is studied. Under a general assumption, we show that if the solution set of a complementarity problem is nonempty, then we can get a solution by the semidefinite relaxation method; while if it does not have a solution, we can obtain a certificate for the infeasibility. Some numerical examples are given.

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Jin-Ling Zhao & Yue-Yang Dai

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  1. Jin-Ling Zhao
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  2. Yue-Yang Dai
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Contributions

In this paper, J.-L. Zhao is in charge of the semidefinite relaxation method for LCPs, NCPs and TCPs, theoretical analysis and paper writing. Y.-Y. Dai is in charge of the numerical experiments.

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Correspondence to Jin-Ling Zhao.

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Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 12171105, 11271206), and the Fundamental Research Funds for the Central Universities (No. FRF-DF-19-004).

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Zhao, JL., Dai, YY. A Semidefinite Relaxation Method for Linear and Nonlinear Complementarity Problems with Polynomials. J. Oper. Res. Soc. China (2023). https://doi.org/10.1007/s40305-023-00491-3

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