A generalized alternating direction method of multipliers for tensor complementarity problems

Kun Liu (), Anwa Zhou () and Jinyan Fan ()
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Kun Liu: Shanghai University
Anwa Zhou: Shanghai University
Jinyan Fan: Shanghai Jiao Tong University

Computational Optimization and Applications, 2024, vol. 88, issue 3, No 7, 903-921

Abstract: Abstract In this paper, we consider the tensor complementarity problem (TCP). From the perspective of non-coupled equality constraint minimization problem for the symmetric TCP, we propose a generalized alternating direction method of multipliers (G-ADMM) to solve the general TCP in which the tensor may not be symmetric. The global convergence and the $$O(\frac{1}{k})$$ O ( 1 k ) convergence rate of the proposed method are proved under the assumption which is much weaker than the monotone assumption. Numerical results show that the method is efficient for solving the TCP.

Keywords: Tensor complementarity problems; Generalized alternating direction method of multipliers; Monotone mapping; Global convergence; 90C30; 90C33; 65K10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00579-3

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