Global linear convergence of a path-following algorithm for some monotone variational inequality problems

1992 ◽  
Vol 75 (2) ◽  
pp. 265-279 ◽  
Author(s):  
P. Tseng
Keyword(s):  
Variational Inequality ◽  
Path Following ◽  
Linear Convergence ◽  
Variational Inequality Problems ◽  
Global Linear Convergence ◽  
Monotone Variational Inequality ◽  
Path Following Algorithm

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).

An Extended Projection Neural Network for Constrained Optimization

2004 ◽  
Vol 16 (4) ◽  
pp. 863-883 ◽  
Author(s):  
Youshen Xia
Keyword(s):  
Neural Network ◽  
Variational Inequality ◽  
Parallel Implementation ◽  
Variational Inequality Problems ◽  
Extended Projection ◽  
Linear And Nonlinear Constraints ◽  
Lower Complexity ◽  
Monotone Variational Inequality ◽  
Projection Neural Network ◽  
Special Case

Recently, a projection neural network has been shown to be a promising computational model for solving variational inequality problems with box constraints. This letter presents an extended projection neural network for solving monotone variational inequality problems with linear and nonlinear constraints. In particular, the proposed neural network can include the projection neural network as a special case. Compared with the modified projection-type methods for solving constrained monotone variational inequality problems, the proposed neural network has a lower complexity and is suitable for parallel implementation. Furthermore, the proposed neural network is theoretically proven to be exponentially convergent to an exact solution without a Lipschitz condition. Illustrative examples show that the extended projection neural network can be used to solve constrained monotone variational inequality problems.

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