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A semidefinite relaxation method for second-order cone polynomial complementarity problems

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Abstract

This paper discusses how to compute all real solutions of the second-order cone tensor complementarity problem when there are finitely many ones. For this goal, we first formulate the second-order cone tensor complementarity problem as two polynomial optimization problems. Based on the reformulation, a semidefinite relaxation method is proposed by solving a finite number of semidefinite relaxations with some assumptions. Numerical experiments are given to show the efficiency of the method.

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Acknowledgements

Xinzhen Zhang was partly supported by the National Natural Science Foundation of China (Grant No. 11871369).

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  1. School of Mathematics, Tianjin University, Tianjin, 300350, China

    Lulu Cheng & Xinzhen Zhang

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  1. Lulu Cheng
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  2. Xinzhen Zhang
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Correspondence to Xinzhen Zhang.

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Cheng, L., Zhang, X. A semidefinite relaxation method for second-order cone polynomial complementarity problems. Comput Optim Appl 75, 629–647 (2020). https://doi.org/10.1007/s10589-019-00162-1

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