The Existence and Uniqueness of Solution of the Vertical Tensor Complementarity Problem

Dan Wang () and Jicheng Li ()
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Dan Wang: Xi’an Jiaotong University
Jicheng Li: Xi’an Jiaotong University

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 3, No 17, 23 pages

Abstract: Abstract For the vertical tensor complementarity problems (VTCPs) and generalized order polynomial complementarity problems (GOPCPs), we make contributions to analyzing some properties of solutions. We propose some types of block tensors mainly based on ER-tensor and P-function, respectively, and use these block tensors to investigate existence and uniqueness of solution of the VTCPs. We also propose conditions for the existence of solution to the VTCPs when all involved tensors are nonnegative. Under mild conditions, the boundeness of the solution set and uniqueness of the solution of the GOPCPs are discussed.

Keywords: Vertical tensor complementarity problem; Vertical polynomial complementarity problem; Type ER; Strong P property; Existence and uniqueness; 90C33; 90C30; 15A69 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02717-1

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