The Existence and Uniqueness of Solution for Tensor Complementarity Problem and Related Systems

Lu-Bin Cui (), Yu-Dong Fan (), Yi-Sheng Song and Shi-Liang Wu ()
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Lu-Bin Cui: Henan Normal University
Yu-Dong Fan: Henan Normal University
Yi-Sheng Song: Chongqing Normal University
Shi-Liang Wu: Yunnan Normal University

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 1, No 13, 334 pages

Abstract: Abstract In the paper, we are concerned with the existence and uniqueness of solution for tensor complementarity problem (TCP) and tensor absolute value equations (TAVEs) with special structure. First, we give a sufficient condition of P tensors by using the nonsingularity of the relevant tensors and the properties of eigenvalues. In addition, we give the conditions for the existence and uniqueness of solution for the TCP and prove that the TAVEs with a special structure are equivalent to the TCP. Based on these, using the equivalence relationship with the TCP, some sufficient conditions for the existence and uniqueness of solution for the TAVEs with special structure are given.

Keywords: Tensor complementarity problem; Existence; Uniqueness; Tensor absolute value equations; Nonsingularity; 15A69; 65F08 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-021-01972-2

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