Generalized Tensor Complementarity Problems Over a Polyhedral Cone

Liyun Ling, Chen Ling () and Hongjin He
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Liyun Ling: Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou 310018, P. R. China2Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China
Chen Ling: Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou 310018, P. R. China
Hongjin He: Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou 310018, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2020, vol. 37, issue 04, 1-23

Abstract: This paper addresses a class of generalized tensor complementarity problems (GTCPs) over a polyhedral cone. As a new generalization of the well-studied tensor complementarity problems (TCPs) in the literature, we first show the nonemptiness of the solution set of GTCPs when the involved tensor is cone ER. Then, we study bounds of solutions, and in addition to deriving a Hölderian local error bound of the problem under consideration. Finally, we reformulate GTCPs over a polyhedral cone as a system of nonlinear equations, which is helpful to employ the Levenberg–Marquardt algorithm for finding a solution of the problem. Some preliminary numerical results show that such an algorithm is efficient for GTCPs.

Keywords: Tensor complementarity problem; cone ER-tensor; polyhedral cone; local error bound; Levenberg–Marquardt algorithm (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0217595920400060

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