scholarly journals Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems

2021 ◽  
Author(s):  
Zheng Zhou ◽  
Bing Tan ◽  
Songxiao Li
Keyword(s):  
Steepest Descent ◽  
Variational Inclusion ◽  
Inclusion Problems ◽  
Descent Algorithms ◽  
Inertial Extrapolation

scholarly journals Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1161
Author(s):  
Jinhua Zhu ◽  
Jinfang Tang ◽  
Shih-sen Chang ◽  
Min Liu ◽  
Liangcai Zhao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Point Problem ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

A new proximal-like algorithm for solving split variational inclusion problems

2021 ◽  
Author(s):  
Dang Van Hieu ◽  
Simeon Reich ◽  
Pham Ky Anh ◽  
Nguyen Hai Ha
Keyword(s):  
Variational Inclusion ◽  
Inclusion Problems

scholarly journals The Modified Inertial Iterative Algorithm for Solving Split Variational Inclusion Problem for Multi-Valued Quasi Nonexpansive Mappings with Some Applications

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 560 ◽  
Author(s):  
Pawicha Phairatchatniyom ◽  
Poom Kumam ◽  
Yeol Je Cho ◽  
Wachirapong Jirakitpuwapat ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Fixed Point ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Inclusion Problem ◽  
Common Elements ◽  
Inclusion Problems ◽  
Variational Inclusion Problem ◽  
Inertial Extrapolation ◽  
Appl Math

Based on the very recent work by Shehu and Agbebaku in Comput. Appl. Math. 2017, we introduce an extension of their iterative algorithm by combining it with inertial extrapolation for solving split inclusion problems and fixed point problems. Under suitable conditions, we prove that the proposed algorithm converges strongly to common elements of the solution set of the split inclusion problems and fixed point problems.

scholarly journals Strong Convergence of a New Iterative Algorithm for Split Monotone Variational Inclusion Problems

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 123 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Iterative Method ◽  
Hilbert Spaces ◽  
Optimization Problem ◽  
Variational Inclusion ◽  
Hierarchical Optimization ◽  
Inclusion Problem ◽  
Inclusion Problems ◽  
Infinite Dimensional ◽  
Variational Inclusion Problem ◽  
General Iterative Method

The main aim of this work is to introduce an implicit general iterative method for approximating a solution of a split variational inclusion problem with a hierarchical optimization problem constraint for a countable family of mappings, which are nonexpansive, in the setting of infinite dimensional Hilbert spaces. Convergence theorem of the sequences generated in our proposed implicit algorithm is obtained under some weak assumptions.

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