scholarly journals A Self-Adaptive Method for Solving a System of Nonlinear Variational Inequalities

2007 ◽  
Vol 2007 ◽  
pp. 1-7
Author(s):  
Chaofeng Shi
Keyword(s):  
Iterative Method ◽  
Variational Inequalities ◽  
Adaptive Method ◽  
New Method ◽  
Computational Results ◽  
Computation Cost ◽  
Self Adaptive

The system of nonlinear variational inequalities (SNVI) is a useful generalization of variational inequalities. Verma (2001) suggested and analyzed an iterative method for solving SNVI. In this paper, we present a new self-adaptive method, whose computation cost is less than that of Verma's method. The convergence of the new method is proved under the same assumptions as Verma's method. Some preliminary computational results are given to illustrate the efficiency of the proposed method.

scholarly journals On Self-Adaptive Method for General Mixed Variational Inequalities

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Abdellah Bnouhachem ◽  
Muhammad Aslam Noor ◽  
Eman H. Al-Shemas
Keyword(s):  
Global Convergence ◽  
Variational Inequalities ◽  
Complementarity Problems ◽  
Adaptive Method ◽  
Computational Results ◽  
Quasivariational Inequalities ◽  
Special Cases ◽  
General Variational Inequalities ◽  
Mixed Variational Inequalities ◽  
Self Adaptive

We suggest and analyze a new self-adaptive method for solving general mixed variational inequalities, which can be viewed as an improvement of the method of (Noor 2003). Global convergence of the new method is proved under the same assumptions as Noor's method. Some preliminary computational results are given to illustrate the efficiency of the proposed method. Since the general mixed variational inequalities include general variational inequalities, quasivariational inequalities, and nonlinear (implicit) complementarity problems as special cases, results proved in this paper continue to hold for these problems.

scholarly journals Explicit Iterative Method for Variational Inequalities on Hadamard Manifolds

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Iterative Method ◽  
Variational Inequalities ◽  
New Method ◽  
Hadamard Manifold ◽  
Hadamard Manifolds ◽  
Auxiliary Principle ◽  
Auxiliary Principle Technique ◽  
Monotonicity Results

An explicit iterative method for solving the variational inequalities on Hadamard manifold is suggested and analyzed using the auxiliary principle technique. The convergence of this new method requires only the partially relaxed strongly monotonicity, which is a weaker condition than monotonicity. Results can be viewed as refinement and improvement of previously known results.

scholarly journals A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point Problems

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2039 ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Maggie Aphane
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Adaptive Method ◽  
Convergence Result ◽  
Null Point ◽  
Fixed Point Problems ◽  
Bounded Linear ◽  
Contraction Method ◽  
Projection And Contraction Method ◽  
Self Adaptive

We introduce a new projection and contraction method with inertial and self-adaptive techniques for solving variational inequalities and split common fixed point problems in real Hilbert spaces. The stepsize of the algorithm is selected via a self-adaptive method and does not require prior estimate of norm of the bounded linear operator. More so, the cost operator of the variational inequalities does not necessarily needs to satisfies Lipschitz condition. We prove a strong convergence result under some mild conditions and provide an application of our result to split common null point problems. Some numerical experiments are reported to illustrate the performance of the algorithm and compare with some existing methods.

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.

A new self-adaptive iterative method for general mixed quasi variational inequalities

2008 ◽  
Vol 28 (3) ◽  
pp. 685-696
Author(s):  
Abdellah Bnouhachem ◽  
Mohamed Khalfaoui ◽  
Hafida Benazza
Keyword(s):  
Iterative Method ◽  
Variational Inequalities ◽  
Self Adaptive

A New Blocking Method with Dynamic Self-Adaptive PSO Applied in Grounding Grid Corrosion Diagnosis

2012 ◽  
Vol 466-467 ◽  
pp. 342-346
Author(s):  
Yi Hui Zheng ◽  
Tian Yu Li ◽  
Li Xue Li ◽  
Gang Yao ◽  
Qing Shan Xu
Keyword(s):  
Work Force ◽  
Adaptive Method ◽  
New Method ◽  
Average Rule ◽  
Grounding Grid ◽  
Adaptive Pso ◽  
Solving Equations ◽  
Searching Ability ◽  
Solution Accuracy ◽  
Self Adaptive

To make Power system safe and stable, corrosion of grounding grid has become one of the most threatened phenomena and problems. With the object of reducing work force and diagnosing the corrosion situations more quickly and exactly, a new method has been proposed based on blocking way with dynamic self-adaptive PSO. First, irregular grids are supposed to be separated into several regular blocks. Then the diagnosis equations will be constructed so that the original ill conditions can be reduced and the solution accuracy will be increased as well. Accordingly, the problem of solving equations should be changed into optimizing solution of problems. In this paper, a new method called Dynamic Self-Adaptive Particle Swarm Optimization (DSAPSO) is proposed, which utilizes an average rule to estimate the whole swarm to divide it into three parts of different conditions, which are called excellent part, self-adaptive part and also worse part. Such a standard principle is based on the evaluation of fitness. Aiming at different groups, their speeds and positions will be updated with different parameters. And also a self-adaptive method has been added into regulation of parameter. Furthermore, such a dynamic method will do favor in increasing the global searching ability and avoiding from calculating complexity. Eventually, the effectiveness and accuracy of the method is verified by the application in a power station in Jilin Province.

New self-adaptive method for image denoising based on sparse decomposition and clustering

2013 ◽  
Vol 33 (2) ◽  
pp. 476-479
Author(s):  
Yali WEI ◽  
Xianbin WEN ◽  
Yongliao ZOU ◽  
Yongchun ZHENG
Keyword(s):  
Image Denoising ◽  
Adaptive Method ◽  
Sparse Decomposition ◽  
Self Adaptive
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