Abstract
Stochastic tensor complementarity problem with discrete distribution is investigated, which is a kind of stochastic tensor complementarity problem with discrete probability distribution variables. First, we formulate the stochastic tensor complementarity problem with discrete distribution as a constrained minimization problem. Some properties of this reformulation are studied based on the structured tensor. Then we propose a new semismooth Newton method for solving this problem. The proposed method combines the semismooth Newton method with the Barzilai–Borwein stepsize technique. In addition, the method uses the nonmonotone linesearch technique to ensure its global convergence. Any accumulation point of the sequence generated by the proposed method approximates to a solution of the stochastic tensor complementarity problem with discrete distribution. Finally, numerical results are given to verify our theoretical results.
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Acknowledgements
The authors would like to thank the handling editor Liqun Qi and Prof. Sanzheng Qiao for their detailed comments on the presentation of our paper. The authors are also grateful to three anonymous referees for their many helpful comments.
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S. Du: This author is supported by the National Natural Science Foundation of China under Grant 11671220. Y. Wei: This author is supported by Innovation Program of Shanghai Municipal Education Commission and the National Natural Science Foundation of China under Grant 11771099.
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Du, S., Cui, L., Chen, Y. et al. Stochastic Tensor Complementarity Problem with Discrete Distribution. J Optim Theory Appl 192, 912–929 (2022). https://doi.org/10.1007/s10957-021-01997-7
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DOI: https://doi.org/10.1007/s10957-021-01997-7
Keywords
- Stochastic tensor complementarity problem
- Semismooth Newton method
- Barzilai–Borwein stepsize
- Convergence