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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| Published in: | Journal of global optimization Vol. 73; no. 4; pp. 789 - 800 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Springer US
15.04.2019
Springer Springer Nature B.V |
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| ISSN: | 0925-5001, 1573-2916 |
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| 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. |
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| AbstractList | 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. |
| Audience | Academic |
| Author | Zhang, Liping Du, Shouqiang |
| Author_xml | – sequence: 1 givenname: Shouqiang surname: Du fullname: Du, Shouqiang organization: School of Mathematics and Statistics, Qingdao University – sequence: 2 givenname: Liping surname: Zhang fullname: Zhang, Liping email: lzhang@math.tsinghua.edu.cn, lipingzhang@tsinghua.edu.cn organization: Department of Mathematical Sciences, Tsinghua University |
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| Keywords | Tensor complementarity problem Positive definite Unique solution Mixed integer programming 15A69 90C11 |
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| SubjectTerms | Computer Science Integer programming Mathematical analysis Mathematics Mathematics and Statistics Mixed integer Operations Research/Decision Theory Optimization Real Functions Tensors |
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| Title | A mixed integer programming approach to the tensor complementarity problem |
| URI | https://link.springer.com/article/10.1007/s10898-018-00731-4 https://www.proquest.com/docview/2162676011 |
| Volume | 73 |
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