Name
Title | ||
|---|---|---|
An Iterative Method for Finding the Least Solution to the Tensor Complementarity Problem. |
Abstract | ||
|---|---|---|
In this paper, we are concerned with finding the least solution to the tensor complementarity problem. When the involved tensor is strongly monotone, we present a way to estimate the nonzero elements of the solution in a successive manner. The procedure for identifying the nonzero elements of the solution gives rise to an iterative method of solving the tensor complementarity problem. In each iteration, we obtain an iterate by solving a lower-dimensional tensor equation. After finitely many iterations, the method terminates with a solution to the problem. Moreover, the sequence generated by the method is monotonically convergent to the least solution to the problem. We then extend this idea for general case and propose a sequential mathematical programming method for finding the least solution to the problem. Since the least solution to the tensor complementarity problem is the sparsest solution to the problem, the method can be regarded as an extension of a recent result by Luo et al. (Optim Lett 11:471–482, 2017). Our limited numerical results show that the method can be used to solve the tensor complementarity problem efficiently. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s10957-017-1157-5 | J. Optimization Theory and Applications |
Keywords | Field | DocType |
Tensor complementarity problem,Z-tensor,Least solution,Sparsest solution,Monotone convergence,90C33,15A72,65N12 | Monotonic function,Mathematical optimization,Tensor (intrinsic definition),Tensor,Iterative method,Mathematical analysis,Strongly monotone,Complementarity theory,Mixed complementarity problem,Mathematics | Journal |
Volume | Issue | ISSN |
175 | 1 | 0022-3239 |
Citations | PageRank | References |
5 | 0.43 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shuilian Xie | 1 | 5 | 0.43 |
| Donghui Li | 2 | 380 | 32.40 |
| Hongru Xu | 3 | 17 | 4.08 |