Journal of the Operations Research Society of China ›› 2025, Vol. 13 ›› Issue (1): 268-286.doi: 10.1007/s40305-023-00491-3

• • 上一篇    下一篇

  

  • 收稿日期:2022-09-02 修回日期:2023-04-17 出版日期:2025-03-30 发布日期:2025-03-20
  • 通讯作者: Jin-Ling Zhao,Yue-Yang Dai E-mail:jlzhao@ustb.edu.cn;xzwydreamer@163.com
  • 基金资助:
    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).

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

Jin-Ling Zhao, Yue-Yang Dai   

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
  • Received:2022-09-02 Revised:2023-04-17 Online:2025-03-30 Published:2025-03-20
  • Contact: Jin-Ling Zhao,Yue-Yang Dai E-mail:jlzhao@ustb.edu.cn;xzwydreamer@163.com

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.

Key words: Semidefinite relaxation, Linear complementarity problem, Nonlinear complementarity problem, Tensor complementarity problem

中图分类号: