Relaxed extragradient algorithm for solving pseudomonotone variational inequalities in Hilbert spaces

Optimization ◽  
2019 ◽  
Vol 69 (10) ◽  
pp. 2279-2304 ◽  
Author(s):  
Dang Van Hieu ◽  
Yeol Je Cho ◽  
Yi-bin Xiao ◽  
Poom Kumam
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Extragradient Algorithm

scholarly journals Halpern subgradient extragradient algorithm for solving quasimonotone variational inequality problems

2021 ◽  
Vol 38 (1) ◽  
pp. 249-262
Author(s):  
PONGSAKORN YOTKAEW ◽  
◽  
HABIB UR REHMAN ◽  
BANCHA PANYANAK ◽  
NUTTAPOL PAKKARANANG ◽  
...  
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Line Search ◽  
Lipschitz Constant ◽  
Iterative Sequence ◽  
Step Size ◽  
Infinite Dimensional ◽  
Extragradient Algorithm ◽  
Line Search Method ◽  
Quasimonotone Operators

In this paper, we study the numerical solution of the variational inequalities involving quasimonotone operators in infinite-dimensional Hilbert spaces. We prove that the iterative sequence generated by the proposed algorithm for the solution of quasimonotone variational inequalities converges strongly to a solution. The main advantage of the proposed iterative schemes is that it uses a monotone and non-monotone step size rule based on operator knowledge rather than its Lipschitz constant or some other line search method.

scholarly journals An Efficient Parallel Extragradient Method for Systems of Variational Inequalities Involving Fixed Points of Demicontractive Mappings

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1915
Author(s):  
Lateef Olakunle Jolaoso ◽  
Maggie Aphane
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Line Search ◽  
Convex Combination ◽  
Extragradient Method ◽  
Convergence Result ◽  
Armijo Line Search ◽  
Systems Of Variational Inequalities ◽  
Demicontractive Mappings ◽  
The Cost

Herein, we present a new parallel extragradient method for solving systems of variational inequalities and common fixed point problems for demicontractive mappings in real Hilbert spaces. The algorithm determines the next iterate by computing a computationally inexpensive projection onto a sub-level set which is constructed using a convex combination of finite functions and an Armijo line-search procedure. A strong convergence result is proved without the need for the assumption of Lipschitz continuity on the cost operators of the variational inequalities. Finally, some numerical experiments are performed to illustrate the performance of the proposed method.

Iterative methods for a class of variational inequalities in Hilbert spaces

2017 ◽  
Vol 19 (4) ◽  
pp. 2383-2395
Author(s):  
Nguyen Buong ◽  
Pham Thi Thu Hoai ◽  
Nguyen Duong Nguyen
Keyword(s):  
Variational Inequalities ◽  
Iterative Methods ◽  
Hilbert Spaces

scholarly journals Nonpivot and Implicit Projected Dynamical Systems on Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Monica Gabriela Cojocaru ◽  
Stephane Pia
Keyword(s):  
Dynamical Systems ◽  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Dual Space ◽  
Variational Problems ◽  
Base Space ◽  
Projected Dynamical Systems

This paper presents a generalization of the concept and uses of projected dynamical systems to the case of nonpivot Hilbert spaces. These are Hilbert spaces in which the topological dual space is not identified with the base space. The generalization consists of showing the existence of such systems and their relation to variational problems, such as variational inequalities. In the case of usual Hilbert spaces these systems have been extensively studied, and, as in previous works, this new generalization has been motivated by applications, as shown below.

Sign in / Sign up

Export Citation Format

Share Document