Generalized proximal-type methods for weak vector variational inequality problems in Banach spaces. (English) Zbl 1338.90375
Summary: In this paper, we propose a class of generalized proximal-type method by the virtue of Bregman functions to solve weak vector variational inequality problems in Banach spaces. We carry out a convergence analysis on the method and prove the weak convergence of the generated sequence to a solution of the weak vector variational inequality problems under some mild conditions. Our results extend some known results to more general cases.
MSC:
| 90C29 | Multi-objective and goal programming |
| 65K10 | Numerical optimization and variational techniques |
| 49M05 | Numerical methods based on necessary conditions |
Keywords:
vector variational inequality problems; proximal-type method; Banach spaces; Bregman functions; weak normal mapping; convergence analysisReferences:
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