English

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 ZZ-tensors (which are tensors with non-positive off-diagonal entries), we describe various equivalent conditions for a ZZ-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.

Keywords

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

R2 v1 2026-06-22T11:30:06.072Z