A mixed integer programming approach to the tensor complementarity problem

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...

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Bibliographic Details
Published in:Journal of global optimization Vol. 73; no. 4; pp. 789 - 800
Main Authors: Du, Shouqiang, Zhang, Liping
Format: Journal Article
Language:English
Published: New York Springer US 15.04.2019
Springer
Springer Nature B.V
Subjects:
Computer Science
Integer programming
Mathematical analysis
Mathematics
Mathematics and Statistics
Mixed integer
Operations Research/Decision Theory
Optimization
Real Functions
Tensors
Tensor complementarity problem
Positive definite
Unique solution
Mixed integer programming
15A69
90C11
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary: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.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-018-00731-4