The sparsest solutions to Z-tensor complementarity problems

Ziyan Luo, Liqun Qi, Naihua Xiu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

126 Citations (Scopus)


Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard due to the nonconvexity and noncontinuity of the involved ℓ0norm. 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.
Original languageEnglish
Pages (from-to)471-482
Number of pages12
JournalOptimization Letters
Issue number3
Publication statusPublished - 1 Mar 2017


  • Exact relaxation
  • Polynomial programming
  • Sparse solution
  • Tensor complementarity problem
  • Z-tensor

ASJC Scopus subject areas

  • Control and Optimization


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