Abstract
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 language | English |
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Pages (from-to) | 471-482 |
Number of pages | 12 |
Journal | Optimization Letters |
Volume | 11 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Mar 2017 |
Keywords
- Exact relaxation
- Polynomial programming
- Sparse solution
- Tensor complementarity problem
- Z-tensor
ASJC Scopus subject areas
- Control and Optimization