Existence results for solutions of mixed tensor variational inequalities
- Resource Type
- Authors
- Jiang-hua Fan; Wenjie Mu
- Source
- Journal of Global Optimization. 82:389-412
- Subject
- Pure mathematics
Class (set theory)
Control and Optimization
Applied Mathematics
Solution set
Positive-definite matrix
Management Science and Operations Research
Characterization (mathematics)
Computer Science Applications
Mixed tensor
Compact space
Convex optimization
Variational inequality
Mathematics
- Language
- ISSN
- 1573-2916
0925-5001
By employing the notion of exceptional family of elements, we establish existence results for the mixed tensor variational inequalities. We show that the nonexistence of an exceptional family of elements is a sufficient condition for the solvability of mixed tensor variational inequality. For positive semidefinite mixed tensor variational inequalities, the nonexistence of an exceptional family of elements is proved to be an equivalent characterization of the nonemptiness of the solution sets. We derive several sufficient conditions of the nonemptiness and compactness of the solution sets for the mixed tensor variational inequalities with some special structured tensors. Finally, we show that the mixed tensor variational inequalities can be defined as a class of convex optimization problems.