The bounds of the solution set for the extended vertical tensor complementarity problem
Applicable Nonlinear Analysis, Volume 3, Issue 2, August 2026, Pages: 114–129
HAI-DAN WEI
School of Mathematical Sciences, Center for Applied Mathematics of Guangxi, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning 530006, China
XUE-LIU LI
School of Mathematics, Guangxi University, Nanning 530004, China
GUO-JI TANG
School of Mathematical Sciences, Center for Applied Mathematics of Guangxi, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning 530006, China
Abstract
In this paper, we investigate the bounds of the solution set for the extended vertical tensor complementarity problem (EVTCP). We first introduce several generalized structural constants for a system of \(l\) tensors, utilizing absolute value products and nested minimum-maximum operators to preserve strict algebraic homogeneity and sign consistency. Based on these newly defined constants, we establish several explicit upper bounds for the solution set of the EVTCP under the conditions that the underlying tensor tuple is an \(EVP\)-tensor tuple or an \(EVR_0\)-tensor tuple. Furthermore, we rigorously compare the sharpness of these proposed upper bounds. The theoretical results elegantly extend and refine the existing bounds from the two-tensor vertical complementarity problem to the generalized multi-tensor case. The results obtained in this paper are extensions of those proposed by Wang-Fu-Wu (J. Optim. Theory Appl., 2025, 204:2) from the vertical tensor complementarity problem (VTCP) to EVTCP.
Cite this Article as
Hai-Dan Wei, Xue-Liu Li, and Guo-Ji Tang, The bounds of the solution set for the extended vertical tensor complementarity problem, Applicable Nonlinear Analysis, 3(2), 114–129, 2026