Extended Horizontal Tensor Complementarity Problems
Sonali Sharma, V. Vetrivel
TL;DR
This work broadens tensor complementarity theory by introducing the Extended Horizontal Tensor Complementarity Problem (EHTCP), a unifying framework that subsumes HTCP and TCP as special cases. By defining new structured tensor classes (EHR0, EHP, EHE, EHND) and leveraging degree theory, the authors establish conditions for nonemptiness and compactness of the solution set, derive a robust EHTCP-degree, and prove existence results. They further show that strong EHP tensors yield uniqueness of solutions, and strong EHND tensors ensure finiteness of the solution set, while highlighting that finiteness may fail in general without such strong conditions. Overall, the paper extends classical LCP/TCP results to a versatile tensor setting, offering theoretical guarantees and a framework for future analysis of EHTCP-related problems.
Abstract
In this paper, we study the nonemptiness, compactness, uniqueness, and finiteness of the solution set of a new type of nonlinear complementarity problem, namely the extended horizontal tensor complementarity problem (EHTCP). We introduce several classes of structured tensors and discuss the interconnections among these tensors. Consequently, we study the properties of the solution set of the EHTCP with the help of degree theory.