Z-tensors and complementarity problems
Optimization and Control
2017-01-02 v2
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 -tensors (which are tensors with non-positive off-diagonal entries), we describe various equivalent conditions for a -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.
Cite
@article{arxiv.1510.07933,
title = {Z-tensors and complementarity problems},
author = {M. Seetharama Gowda and Ziyan Luo and Liqun Qi and Naihua Xiu},
journal= {arXiv preprint arXiv:1510.07933},
year = {2017}
}
Comments
12 pages. Some results and proofs are modified, and references are updated. Concluding remarks are added