期刊
OPTIMIZATION LETTERS
卷 11, 期 3, 页码 471-482出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s11590-016-1013-9
关键词
Z-tensor; Tensor complementarity problem; Sparse solution; Exact relaxation; Polynomial programming
资金
- National Natural Science Foundation of China [11301022, 11431002]
- State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University [RCS2014ZT20, RCS2014ZZ01]
- Hong Kong Research Grant Council [PolyU 502111, 501212, 501913, 15302114]
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 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.
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