Z-tensors and complementarity problems

Abstract

Tensors are multidimensional analogs of matrices. In this paper, based on degree-theoretic ideas, we study homogeneous nonlinear complementarity problems induced by tensors. By specializing this to $Z$-tensors (which are tensors with non-positive off-diagonal entries), we describe various equivalent conditions for a $Z$-tensor to have the global solvability property. We show by an example that the global solvability need not imply unique solvability and provide a sufficient and easily checkable condition for unique solvability.

12 pages. Some results and proofs are modified, and references are updated. Concluding remarks are added

References in corpus (3)

• Properties of Solution set of Tensor Complementarity Problem
• Polynomial complementarity problems
• P-Tensors, P${}_0$-Tensors, and Tensor Complementarity Problem

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