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- Title
Stability of Solutions and Continuity of Solution Maps of Tensor Complementarity Problems.
- Authors
Bai, Xue-Li; Huang, Zheng-Hai; Li, Xia
- Abstract
Recently, tensor complementarity problems are becoming more and more popular. There are various literatures considering all kinds of properties of tensor complementarity problems, however, the stability of solutions and the continuity of solution maps are rarely mentioned so far. In the present paper, we study these two properties for tensor complementarity problems. We propose conditions under which the solutions of tensor complementarity problems are stable with the help of the tensor variational inequality or structured tensors. We also show that the solution maps of tensor complementarity problems are upper semicontinuous with the involved tensors being R 0 -tensors. Meanwhile, we establish the relationship between the uniqueness of solutions and the continuity of solution maps of tensor complementarity problems.
- Subjects
TENSOR algebra; PERTURBATION theory; PROBLEM solving; UNIQUENESS (Mathematics); MATHEMATICAL equivalence
- Publication
Asia-Pacific Journal of Operational Research, 2019, Vol 36, Issue 2, pN.PAG
- ISSN
0217-5959
- Publication type
Article
- DOI
10.1142/S0217595919400025