On the equivalence between strong solvability and strict semimonotonicity for some systems involving Z-functions

This paper focuses on the relationship between the strong solvability of a certain system involving a Z-function, and the strict semimonotonicity of such a function. Our main result shows that, for a system defined by a continuous, superhomogeneous Z-function, the additional condition of strict semimonotonicity is both necessary and sufficient for strong solvability.     

Solution structures of tensor complementarity problem

We introduce two new types of tensors called the strictly semimonotone tensor and the range column sufficient tensor and explore their structure properties. Based on the obtained results, we make a characterization to the solution of tensor complementarity problem.     

Co-NP-completeness of some matrix classification problems

The classes of P-, P ₀-, R ₀-, semimonotone, strictly semimonotone, column sufficient, and nondegenerate matrices play important roles in studying solution properties of equations and complementarity problems and convergence/complexity analysis of methods for solving these problems. It is known that the problem of deciding whether a square matrix with integer/rational entries is a P- (or nondegenerate) matrix is co-NP-complete. We show, through a unified analysis, that analogous decision problems for the other matrix classes are also co-NP-complete. Received: April 1999 / Accepted: March 1, 2000?Published online May 12, 2000