scholarly journals The Maximum Norm Analysis of Schwarz Method for Elliptic Quasi-Variational Inequalities

2021 ◽  
Vol 45 (4) ◽  
pp. 635-645
Author(s):  
MOHAMMED BEGGAS ◽  
◽  
MOHAMMED HAIOUR ◽  
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Maximum Norm ◽  
Schwarz Method ◽  
Quasi Variational Inequality

In this paper, we present a maximum norm analysis of an overlapping Schwartz method on non matching grids for a quasi-variational inequality, where the obstacle and the second member depend on the solution. Our result improves and generalizes some previous results.

scholarly journals Some New Classes of Extended General Mixed Quasi-Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Auxiliary Principle ◽  
Existence Of A Solution ◽  
Auxiliary Principle Technique ◽  
New Class ◽  
Special Cases ◽  
Quasi Variational Inequality

We consider and study a new class of variational inequality, which is called the extended general mixed quas-variational inequality. We use the auxiliary principle technique to study the existence of a solution of the extended general mixed quasi-variational inequality. Several special cases are also discussed. Results proved in this paper may stimulate further research in this area.

scholarly journals Certain remarks on a class of evolution quasi-variational inequalities

2000 ◽  
Vol 24 (12) ◽  
pp. 851-855 ◽  
Author(s):  
A. H. Siddiqi ◽  
Pammy Manchanda
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Existence Theorems ◽  
Static Problem ◽  
The Other ◽  
Time Dependent ◽  
Isotropic Hardening ◽  
Quasi Variational Inequality

We prove two existence theorems, one for evolution quasi-variational inequalities and the other for a time-dependent quasi-variational inequality modeling the quasi-static problem of elastoplasticity with combined kinetic-isotropic hardening.

scholarly journals Solving Adaptive Image Restoration Problems via a Modified Projection Algorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Hao Yang ◽  
Xueping Luo ◽  
Leiting Chen
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Image Restoration ◽  
Image Denoising ◽  
Existence And Uniqueness ◽  
Experimental Results ◽  
Projection Algorithm ◽  
Tv Regularization ◽  
Uniqueness Of The Solution ◽  
Quasi Variational Inequality

We introduce a new general TV regularizer, namely, generalized TV regularization, to study image denoising and nonblind image deblurring problems. In order to discuss the generalized TV image restoration with solution-driven adaptivity, we consider the existence and uniqueness of the solution for mixed quasi-variational inequality. Moreover, the convergence of a modified projection algorithm for solving mixed quasi-variational inequalities is also shown. The corresponding experimental results support our theoretical findings.

scholarly journals Existence of a solution of the quasi-variational inequality with semicontinuous operator

2006 ◽  
Vol 16 (2) ◽  
pp. 147-152
Author(s):  
Djurica Jovanov
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Existence Of A Solution ◽  
Feasible Set ◽  
Quasi Variational Inequality

The paper considers quasi-variational inequalities with point to set operator. The existence of a solution, in the case when the operator of the quasi-variational inequality is semi-continuous and the feasible set is convex and compact, is proved.

scholarly journals On generalised mixed co-quasi-variational inequalities with noncompact valued mappings

2004 ◽  
Vol 70 (1) ◽  
pp. 7-15
Author(s):  
Rais Ahmad ◽  
Qamrul Hasan Ansari ◽  
Syed Shakaib Irfan
Keyword(s):  
Exact Solution ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Iterative Algorithm ◽  
Approximate Solutions ◽  
Special Cases ◽  
Quasi Variational Inequality

In this paper, we consider generalised mixed co-quasi-variational inequalities with noncompact valued mappings and propose an iterative algorithm for computing their approximate solutions. We prove that the approximate solutions obtained by the proposed algorithm converge to the exact solution of our co-quasi-variational inequality. Some special cases are also discussed.

scholarly journals On Gap Functions for Quasi-Variational Inequalities

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Kouichi Taji
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Gap Function ◽  
Gap Functions ◽  
Merit Functions ◽  
Regularized Gap Function ◽  
Generalized Equilibrium ◽  
Quasi Variational Inequality

For variational inequalities, various merit functions, such as the gap function, the regularized gap function, the D-gap function and so on, have been proposed. These functions lead to equivalent optimization formulations and are used to optimization-based methods for solving variational inequalities. In this paper, we extend the regularized gap function and the D-gap functions for a quasi-variational inequality, which is a generalization of the variational inequality and is used to formulate generalized equilibrium problems. These extensions are shown to formulate equivalent optimization problems for quasi-variational inequalities and are shown to be continuous and directionally differentiable.

QUASI-VARIATIONAL INEQUALITIES IN TRANSPORTATION NETWORKS

2004 ◽  
Vol 14 (10) ◽  
pp. 1541-1560 ◽  
Author(s):  
LAURA SCRIMALI
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Transportation Networks ◽  
User Equilibrium ◽  
Equivalent Formulation ◽  
Equilibrium Conditions ◽  
Delay Effects ◽  
Quasi Variational Inequality

This paper aims to consider user equilibrium problems in transportation networks in the most complete and realistic situations. In fact, the presented model allows for the dependence of data on time, the presence of elastic travel demands, the capacity restrictions and delay effects. The equilibrium conditions for such a model are given and the equivalent formulation in terms of a quasi-variational inequality is discussed. Moreover, a theorem for the existence of solutions is shown and a numerical example is provided. Finally, some questions of stability are studied.

scholarly journals On a Class of Differential Variational Inequalities in Infinite-Dimensional Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 266 ◽  
Author(s):  
Savin Treanţă
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Optimal Control Theory ◽  
Infinite Dimensional ◽  
Nash Games ◽  
New Class ◽  
Set Valued Mappings ◽  
Differential Variational Inequalities ◽  
Theoretical Developments

A new class of differential variational inequalities (DVIs), governed by a variational inequality and an evolution equation formulated in infinite-dimensional spaces, is investigated in this paper. More precisely, based on Browder’s result, optimal control theory, measurability of set-valued mappings and the theory of semigroups, we establish that the solution set of DVI is nonempty and compact. In addition, the theoretical developments are accompanied by an application to differential Nash games.

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