Convergence of Two-Stage Method with Bregman Divergence for Solving Variational Inequalities*

2019 ◽  
Vol 55 (3) ◽  
pp. 359-368 ◽  
Author(s):  
D. A. Nomirovskii ◽  
B. V. Rublyov ◽  
V. V. Semenov
Keyword(s):  
Variational Inequalities ◽  
Bregman Divergence ◽  
Two Stage

scholarly journals Halpern-type relaxed inertial algorithms with Bregman divergence for solving variational inequalities

2021 ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Pongsakorn Sunthrayuth ◽  
Prasit Cholamjiak ◽  
Yeol Je Cho
Keyword(s):  
Applied Sciences ◽  
Variational Inequalities ◽  
Lipschitz Continuity ◽  
Real Hilbert Space ◽  
Extragradient Method ◽  
Weak Continuity ◽  
Subgradient Extragradient Method ◽  
Bregman Divergence ◽  
Effective Technique ◽  
Tseng’S Extragradient Method

Abstract It is well-known that the use of Bregman divergence is an elegant and effective technique for solving many problems in applied sciences. In this paper, we introduce and analyze two new inertial-like algorithms with Bregman divergence for solving pseudomonotone variational inequalities in a real Hilbert space. The first algorithm is inspired by Halpern -type iteration and subgradient extragradient method and the second algorithm is inspired by Halpern -type iteration and Tseng's extragradient method. Under suitable conditions, the strong convergence theorems of the algorithms are established without assuming the Lipschitz continuity and the sequential weak continuity of any mapping. Finally, several numerical experiments with various types of Bregman divergence are also performed to illustrate the theoretical analysis. The results presented in this paper improve and generalize the related works in the literature.

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