scholarly journals A self-adaptive Armijo-like step size method for solving monotone variational inequality problems in Hilbert spaces

2019 ◽  
Vol 2019 (1) ◽  
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Variational Inequality Problems ◽  
Step Size ◽  
Monotone Variational Inequality ◽  
Self Adaptive

scholarly journals Two modifications of the inertial Tseng extragradient method with self-adaptive step size for solving monotone variational inequality problems

2020 ◽  
Vol 53 (1) ◽  
pp. 208-224 ◽  
Author(s):  
Timilehin Opeyemi Alakoya ◽  
Lateef Olakunle Jolaoso ◽  
Oluwatosin Temitope Mewomo
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Extragradient Method ◽  
Lipschitz Constant ◽  
Monotone Mapping ◽  
Variational Inequality Problems ◽  
Step Size ◽  
Lipschitz Continuous ◽  
Convergence Results ◽  
Monotone Variational Inequality

AbstractIn this work, we introduce two new inertial-type algorithms for solving variational inequality problems (VIPs) with monotone and Lipschitz continuous mappings in real Hilbert spaces. The first algorithm requires the computation of only one projection onto the feasible set per iteration while the second algorithm needs the computation of only one projection onto a half-space, and prior knowledge of the Lipschitz constant of the monotone mapping is not required in proving the strong convergence theorems for the two algorithms. Under some mild assumptions, we prove strong convergence results for the proposed algorithms to a solution of a VIP. Finally, we provide some numerical experiments to illustrate the efficiency and advantages of the proposed algorithms.

A new self-adaptive algorithm for solving pseudomonotone variational inequality problems in Hilbert spaces

Optimization ◽  
2021 ◽  
pp. 1-25
Author(s):  
Thong Duong Viet ◽  
Luong Van Long ◽  
Xiao-Huan Li ◽  
Qiao-Li Dong ◽  
Yeol Je Cho ◽  
...  
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Adaptive Algorithm ◽  
Variational Inequality Problems ◽  
Self Adaptive

scholarly journals On the $O(1/k)$ Convergence Rate of He's Alternating Directions Method for a Kind of Structured Variational Inequality Problem

2015 ◽  
Vol 7 (2) ◽  
pp. 69
Author(s):  
Haiwen Xu
Keyword(s):  
Variational Inequality ◽  
Convergence Rate ◽  
Variational Inequality Problem ◽  
Variational Inequality Problems ◽  
System Of Nonlinear Equations ◽  
Inequality Problem ◽  
Quadratic Minimization ◽  
Projection And Contraction Methods ◽  
Monotone Variational Inequality ◽  
Alternating Directions Method

The  alternating directions method for a kind of structured variational inequality problem (He, 2001) is an attractive method for structured monotone variational inequality problems. In each iteration, the subproblemsare  convex quadratic minimization problem with simple constraintsand a well-conditioned system of nonlinear equations that can be efficiently solvedusing classical methods. Researchers have recently described the convergence rateof projection and contraction methods for variational inequality problems andthe original ADM and its linearized variant. Motivated and inspired by researchinto the convergence rate of these methods, we provide a simple proof to show the $O(1/k)$ convergencerate of  alternating directions methods for structured monotone variational inequality problems (He, 2001).

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