Finite termination of a smoothing-type algorithm for the monotone affine variational inequality problem

2009 ◽  
Vol 211 (1) ◽  
pp. 177-184 ◽  
Author(s):  
Ping Wang ◽  
Na Zhao
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Finite Termination ◽  
Inequality Problem ◽  
Affine Variational Inequality ◽  
Type Algorithm

scholarly journals Stability and Convergence Analysis for Set-Valued Extended Generalized Nonlinear Mixed Variational Inequality Problems and Generalized Resolvent Dynamical Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Iqbal Ahmad ◽  
Zahoor Ahmad Rather ◽  
Rais Ahmad ◽  
Ching-Feng Wen
Keyword(s):  
Dynamical System ◽  
Variational Inequality ◽  
Iterative Algorithm ◽  
Variational Inequality Problem ◽  
Stability And Convergence ◽  
Mixed Variational Inequality ◽  
Generalized Resolvent ◽  
Inequality Problem ◽  
System A ◽  
Type Algorithm

In this paper, we study a set-valued extended generalized nonlinear mixed variational inequality problem and its generalized resolvent dynamical system. A three-step iterative algorithm is constructed for solving set-valued extended generalized nonlinear variational inequality problem. Convergence and stability analysis are also discussed. We have shown the globally exponential convergence of generalized resolvent dynamical system to a unique solution of set-valued extended generalized nonlinear mixed variational inequality problem. In support of our main result, we provide a numerical example with convergence graphs and computation tables. For illustration, a comparison of our three-step iterative algorithm with Ishikawa-type algorithm and Mann-type algorithm is shown.

scholarly journals Topological degree and application to a parabolic variational inequality problem

2001 ◽  
Vol 25 (4) ◽  
pp. 273-287 ◽  
Author(s):  
A. Addou ◽  
B. Mermri
Keyword(s):  
Variational Inequality ◽  
Topological Degree ◽  
Variational Inequality Problem ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Parabolic Variational Inequality ◽  
Inequality Problem ◽  
Monotone Map ◽  
New Formulation

We are interested in constructing a topological degree for operators of the formF=L+A+S, whereLis a linear densely defined maximal monotone map,Ais a bounded maximal monotone operators, andSis a bounded demicontinuous map of class(S+)with respect to the domain ofL. By means of this topological degree we prove an existence result that will be applied to give a new formulation of a parabolic variational inequality problem.

scholarly journals A Mean Extragradient Method for Solving Variational Inequalities

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 462
Author(s):  
Apichit Buakird ◽  
Nimit Nimana ◽  
Narin Petrot
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Weak Convergence ◽  
Numerical Experiments ◽  
Variational Inequality Problem ◽  
Extragradient Method ◽  
Mean Value ◽  
Inequality Problem ◽  
The Mean ◽  
Mean Value Method

We propose a modified extragradient method for solving the variational inequality problem in a Hilbert space. The method is a combination of the well-known subgradient extragradient with the Mann’s mean value method in which the updated iterate is picked in the convex hull of all previous iterates. We show weak convergence of the mean value iterate to a solution of the variational inequality problem, provided that a condition on the corresponding averaging matrix is fulfilled. Some numerical experiments are given to show the effectiveness of the obtained theoretical result.

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