A mixed integer programming approach to the tensor complementarity problem

Shouqiang Du and Liping Zhang ()
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Shouqiang Du: Qingdao University
Liping Zhang: Tsinghua University

Journal of Global Optimization, 2019, vol. 73, issue 4, No 5, 789-800

Abstract: Abstract The tensor complementarity problem is a special instance of nonlinear complementarity problems, which has many applications. How to solve the tensor complementarity problem, via analyzing the structure of the related tensor, is one of very important research issues. In this paper, we propose a mixed integer programming approach for solving the tensor complementarity problem. We reformulate the tensor complementarity problem as an equivalent mixed integer feasibility problem. Based on the reformulation, some conditions for the solution existence and some solution properties of the tensor complementarity problem are given. We also prove that the tensor complementarity problem, corresponding to a positive definite diagonal tensor, has a unique solution. Finally, numerical results are reported to indicate the efficiency of the proposed algorithm.

Keywords: Tensor complementarity problem; Mixed integer programming; Unique solution; Positive definite; 15A69; 90C11 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (13)

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DOI: 10.1007/s10898-018-00731-4

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