Solvability of Two Classes of Tensor Complementarity Problems. (4th March 2019)

• Record Type: Journal Article
• Authors: Xu, Yang; Gu, Weizhe; Huang, He
• Other Names: Kalashnikov Vyacheslav Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2019(2019)
• Publication Date: 2019-03-04
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2019/6107517
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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 aD -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.