scholarly journals An Improved Two-Step Method for Generalized Variational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Haibin Chen
Keyword(s):  
Variational Inequalities ◽  
Error Bound ◽  
Point Of View ◽  
Large Decrease ◽  
Step Method ◽  
Generalized Variational Inequalities ◽  
Mild Conditions ◽  
Extragradient Algorithm ◽  
Globally Convergent ◽  
Geometric Point

We propose an improved two-step extragradient algorithm for pseudomonotone generalized variational inequalities. It requires two projections at each iteration and allows one to take different stepsize rules. Moreover, from a geometric point of view, it is shown that the new method has a long stepsize, and it guarantees that the distance from the next iterative point to the solution set has a large decrease. Under mild conditions, we show that the method is globally convergent, and then the R-linearly convergent property of the method is proven if a projection-type error bound holds locally.

NEW THREE-STEP ITERATIVE METHOD FOR SOLVING MIXED VARIATIONAL INEQUALITIES

2011 ◽  
Vol 08 (01) ◽  
pp. 139-150
Author(s):  
ABDELLAH BNOUHACHEM ◽  
MUHAMMAD ASLAM NOOR ◽  
ZHAOHAN SHENG ◽  
EISA AL-SAID
Keyword(s):  
Iterative Method ◽  
Variational Inequalities ◽  
Numerical Experiments ◽  
New Method ◽  
Descent Direction ◽  
Mild Conditions ◽  
Globally Convergent ◽  
Special Cases ◽  
Mixed Variational Inequalities

In this paper, we suggest and analyze a new three-step iterative method for solving mixed variational inequalities. The new iterate is obtained by using a descent direction. We prove that the new method is globally convergent under suitable mild conditions. Our results can be viewed as significant extensions of the previously known results for mixed variational inequalities. Since mixed variational inequalities include variational inequalities as special cases, our method appears to be a new one for solving variational inequalities. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method.

scholarly journals Extended Extragradient Methods for Generalized Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yonghong Yao ◽  
Yeong-Cheng Liou ◽  
Cun-Lin Li ◽  
Hui-To Lin
Keyword(s):  
Banach Space ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Extragradient Method ◽  
Extragradient Methods ◽  
Generalized Variational Inequalities ◽  
Mild Conditions ◽  
Convergence Results ◽  
Special Cases

We suggest a modified extragradient method for solving the generalized variational inequalities in a Banach space. We prove some strong convergence results under some mild conditions on parameters. Some special cases are also discussed.

THREE-STEP PROJECTION METHOD FOR GENERAL VARIATIONAL INEQUALITIES

2012 ◽  
Vol 26 (13) ◽  
pp. 1250066 ◽  
Author(s):  
ABDELLAH BNOUHACHEM ◽  
MUHAMMAD ASLAM NOOR
Keyword(s):  
Variational Inequalities ◽  
Projection Method ◽  
New Method ◽  
Descent Direction ◽  
Mild Conditions ◽  
Globally Convergent ◽  
General Variational Inequalities ◽  
Iterative Projection Method

In this paper, we suggest and analyze a new three-step iterative projection method for solving general variational inequalities in conjunction with a descent direction. We prove that the new method is globally convergent under suitable mild conditions. An example is given to illustrate the advantage and efficiency of the proposed method.

scholarly journals Laws of the iterated logarithm on covering graphs with groups of polynomial volume growth

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ryuya Namba
Keyword(s):  
Random Walks ◽  
Quadratic Forms ◽  
Volume Growth ◽  
Moderate Deviation ◽  
Point Of View ◽  
Iterated Logarithm ◽  
Large Numbers ◽  
Geometric Point ◽  
Rate Functions ◽  
The Given

AbstractModerate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any intermediate spatial scalings between those of laws of large numbers and those of central limit theorems. The corresponding rate functions are given by quadratic forms determined by the Albanese metric associated with the given random walks. We apply MDPs to establish laws of the iterated logarithm on the covering graphs by characterizing the set of all limit points of the normalized random walks.

Dynamics of Multibody Systems: Generalized Mass Metric in Riemannian Velocity Space and Recursive Momentum Formulation

2007 ◽  
Author(s):  
Qiang Zhao ◽  
Hong Tao Wu
Keyword(s):  
Point Of View ◽  
Velocity Space ◽  
Motion Equations ◽  
Closed Loop Systems ◽  
Dynamics Of Multibody Systems ◽  
Operator Factorization ◽  
Geometric Point ◽  
Mass Tensor ◽  
Generalized Momentum ◽  
Serial Chains

This paper describes two aspects of multibody system (MBS) dynamics on a generalized mass metric in Riemannian velocity space and recursive momentum formulation. Firstly, we present a detailed expression of the Riemannian metric and operator factorization of a generalized mass tensor for the dynamics of general-topology rigid MBS. The derived expression allows a clearly understanding the components of the generalized mass tensor, which also constitute a metric of the Riemannian velocity space. It is being the fact that there does exist a common metric in Lagrange and recursive Newton-Euler dynamic equation, we can determine, from the Riemannian geometric point of view, that there is the equivalent relationship between the two approaches to a given MBS. Next, from the generalized momentum definition in the derivation of the Riemannian velocity metrics, recursive momentum equations of MBS dynamics are developed for progressively more complex systems: serial chains, topological trees, and closed-loop systems. Through the principle of impulse and momentum, a new method is proposed for reorienting and locating the MBS form a given initial orientation and location to desired final ones without needing to solve the motion equations.

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