The Sparsest Solutions to Z-Tensor Complementarity Problems

2015/05/05 by Ziyan Luo, Liqun Qi, Luo, Ziyan +3 · 3 citations
Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Spectral Theory (math.SP) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1505.00993

openalex publication_date 2015/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard due to the nonconvexity and noncontinuity of the involved ℓ₀ norm. In this paper, a special type of tensor complementarity problems with Z-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.

Citations

• Tensor Decompositions and Applications
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces

Cited by

• Exceptionally Regular Tensors and Tensor Complementarity Problems
• Doubly Nonnegative Tensors, Completely Positive Tensors and Applications
• A Semismooth Newton Method for Tensor Eigenvalue Complementarity Problem
• SOS Tensor Decomposition: Theory and Applications
• Introduction to Tensor Variational Inequalities

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• On sparse solution of tensor complementarity problem
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• Properties of the solution set of generalized polynomial complementarity problems