The Sparsest Solutions to $Z$-Tensor Complementarity Problems
Spectral Theory
2015-05-06 v1 Optimization and Control
Abstract
Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard due to the nonconvexity and noncontinuity of the involved norm. In this paper, a special type of tensor complementarity problems with -tensors has been considered. Under some mild conditions, we show that to pursuit the sparsest solutions is equivalent to solving polynomial programming with a linear objective function. The involved conditions guarantee the desired exact relaxation and also allow to achieve a global optimal solution to the relaxed nonconvex polynomial programming problem. Particularly, in comparison to existing exact relaxation conditions, such as RIP-type ones, our proposed conditions are easy to verify.
Cite
@article{arxiv.1505.00993,
title = {The Sparsest Solutions to $Z$-Tensor Complementarity Problems},
author = {Ziyan Luo and Liqun Qi and Naihua Xiu},
journal= {arXiv preprint arXiv:1505.00993},
year = {2015}
}