Open AccessSolvability of Two Classes of Tensor Complementarity Problems
Author(s) -
Xu Yang,
Wei-Zhe Gu,
Haiyan He
Publication year - 2019
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2019/6107517
Subject(s) - complementarity (molecular biology) , complementarity theory , mathematics , conic optimization , positive definite matrix , regular polygon , tensor (intrinsic definition) , conic section , bounded function , solution set , pure mathematics , combinatorics , convex set , convex optimization , mathematical analysis , set (abstract data type) , computer science , geometry , physics , genetics , eigenvalues and eigenvectors , quantum mechanics , nonlinear system , biology , programming language
In this paper, we first introduce a class of tensors, called positive semidefinite plus tensors on a closed cone, and discuss its simple properties; and then, we focus on investigating properties of solution sets of two classes of tensor complementarity problems. We study the solvability of a generalized tensor complementarity problem with a D -strictly copositive tensor and a positive semidefinite plus tensor on a closed cone and show that the solution set of such a complementarity problem is bounded. Moreover, we prove that a related conic tensor complementarity problem is solvable if the involved tensor is positive semidefinite on a closed convex cone and is uniquely solvable if the involved tensor is strictly positive semidefinite on a closed convex cone. As an application, we also investigate a static traffic equilibrium problem which is reformulated as a concerned complementarity problem. A specific example is also given.