Minty Variational Inequality and Optimization: Scalar and Vector Case

2006 ◽  
pp. 193-211 ◽  
Author(s):  
Giovanni P. Crespi ◽  
Angelo Guerraggio ◽  
Matteo Rocca
Keyword(s):  
Variational Inequality ◽  
Minty Variational Inequality ◽  
Vector Case

On variational inequalities and nonlinear programming problem

2008 ◽  
Vol 45 (4) ◽  
pp. 483-491
Author(s):  
Vsevolod Ivanov
Keyword(s):  
Variational Inequality ◽  
Nonlinear Programming ◽  
Variational Inequalities ◽  
Programming Problem ◽  
Directional Derivative ◽  
Nonlinear Programming Problem ◽  
Solution Sets ◽  
Minty Variational Inequality ◽  
Stampacchia Variational Inequality ◽  
Dini Directional Derivative

In this paper the Stampacchia variational inequality, the Minty variational inequality, and the respective nonlinear programming problem are investigated in terms of the lower Dini directional derivative. We answer the questions which are the largest classes of functions such that the solution sets of each pair of these problems coincide.

On an Euler-Lagrange equation for color to grayscale conversion

2019 ◽  
Vol 2019 (1) ◽  
pp. 95-98
Author(s):  
Hans Jakob Rivertz
Keyword(s):  
Variational Inequality ◽  
Color Image ◽  
Lagrange Equation ◽  
New Method ◽  
Grayscale Image ◽  
Structure Tensors

In this paper we give a new method to find a grayscale image from a color image. The idea is that the structure tensors of the grayscale image and the color image should be as equal as possible. This is measured by the energy of the tensor differences. We deduce an Euler-Lagrange equation and a second variational inequality. The second variational inequality is remarkably simple in its form. Our equation does not involve several steps, such as finding a gradient first and then integrating it. We show that if a color image is at least two times continuous differentiable, the resulting grayscale image is not necessarily two times continuous differentiable.

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 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.

scholarly journals Iterative Computation for Solving the Variational Inequality and the Generalized Equilibrium Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Xiujuan Pan ◽  
Shin Min Kang ◽  
Young Chel Kwun
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Convergence Result ◽  
Generalized Equilibrium Problem ◽  
Iterative Computation ◽  
Generalized Equilibrium

An iterative algorithm for solving the variational inequality and the generalized equilibrium problem has been introduced. Convergence result is given.

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