TY - JOUR
T1 - Analysis of two versions of relaxed inertial algorithms with Bregman divergences for solving variational inequalities
AU - Jolaoso, Lateef Olakunle
AU - Sunthrayuth, Pongsakorn
AU - Cholamjiak, Prasit
AU - Cho, Yeol Je
N1 - Publisher Copyright:
© 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.
PY - 2022/10
Y1 - 2022/10
N2 - In this paper, we introduce and analyze two new inertial-like algorithms with the Bregman divergences for solving the pseudomonotone variational inequality problem in a real Hilbert space. The first algorithm is inspired by the Halpern-type iteration and the subgradient extragradient method and the second algorithm is inspired by the Halpern-type iteration and Tseng’s extragradient method. Under suitable conditions, we prove some strong convergence theorems of the proposed algorithms without assuming the Lipschitz continuity and the sequential weak continuity of the given mapping. Finally, we give some numerical experiments with various types of Bregman divergence to illustrate the main results. In fact, the results presented in this paper improve and generalize the related works in the literature.
AB - In this paper, we introduce and analyze two new inertial-like algorithms with the Bregman divergences for solving the pseudomonotone variational inequality problem in a real Hilbert space. The first algorithm is inspired by the Halpern-type iteration and the subgradient extragradient method and the second algorithm is inspired by the Halpern-type iteration and Tseng’s extragradient method. Under suitable conditions, we prove some strong convergence theorems of the proposed algorithms without assuming the Lipschitz continuity and the sequential weak continuity of the given mapping. Finally, we give some numerical experiments with various types of Bregman divergence to illustrate the main results. In fact, the results presented in this paper improve and generalize the related works in the literature.
KW - Bregman divergence
KW - Hilbert space
KW - Pseudomonotone mapping
KW - Strong convergence
KW - Variational inequality problem
UR - http://www.scopus.com/inward/record.url?scp=85137544670&partnerID=8YFLogxK
U2 - 10.1007/s40314-022-02006-x
DO - 10.1007/s40314-022-02006-x
M3 - Article
AN - SCOPUS:85137544670
SN - 2238-3603
VL - 41
JO - Computational and Applied Mathematics
JF - Computational and Applied Mathematics
IS - 7
M1 - 300
ER -