The sparsest solutions to Z-tensor complementarity problems

Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard due to the nonconvexity and noncontinuity of the involved ℓ 0 norm. In this paper, a special type of tensor complementarity problems with Z -tensors has been considered. Under some mild conditions, we show that t...

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Bibliographic Details
Published in:Optimization letters 2017-03, Vol.11 (3), p.471-482
Main Authors: Luo, Ziyan, Qi, Liqun, Xiu, Naihua
Format: Article
Language:English
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
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Summary:Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard due to the nonconvexity and noncontinuity of the involved ℓ 0 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.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-016-1013-9