Solvability of Two Classes of Tensor Complementarity Problems

Abstract EN

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.