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Generalized Tensor Complementarity Problems Over a Polyhedral Cone

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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)

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.

Suggested Citation

  • Liyun Ling & Chen Ling & Hongjin He, 2020. "Generalized Tensor Complementarity Problems Over a Polyhedral Cone," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(04), pages 1-23, August.
    • Handle: RePEc:wsi:apjorx:v:37:y:2020:i:04:n:s0217595920400060
    DOI: 10.1142/S0217595920400060
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    Cited by:

    1. Tong-tong Shang & Jing Yang & Guo-ji Tang, 2022. "Generalized Polynomial Complementarity Problems over a Polyhedral Cone," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 443-483, February.

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