Abstract
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.
Highlights
1 Introduction The well-known proximal point algorithm (PPA, for short) is a powerful tool for solving optimization problems and variational inequality problems, which was first introduced by Martinet [ ] and its celebrated progress was attained in the work of Rockafellar [ ]
Motivated by [, ], in this paper we propose a class of generalized proximal-type methods by virtue of the Bregman function for solving weak vector variational inequality problems in Banach spaces
4 Conclusions In this paper, we proposed a class of generalized proximal-type method by virtue of the Bregman distance functions to solve weak vector variational inequality problems in Banach spaces
Summary
The well-known proximal point algorithm (PPA, for short) is a powerful tool for solving optimization problems and variational inequality problems, which was first introduced by Martinet [ ] and its celebrated progress was attained in the work of Rockafellar [ ]. Motivated by [ , ], in this paper we propose a class of generalized proximal-type methods by virtue of the Bregman function for solving weak vector variational inequality problems in Banach spaces. We carry out a convergence analysis of the method and prove convergence of the generated sequence to a solution of the weak vector variational inequality problems under some mild conditions.
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