A Projection-Type Method for Set Valued Variational Inequality Problems on Hadamard Manifolds

2016 ◽  
Vol 13 (6) ◽  
pp. 3939-3953
Author(s):  
S. Jana ◽  
C. Nahak
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problems ◽  
Hadamard Manifolds ◽  
Type Method

scholarly journals ρ-PROJECTIVE AND σ-INVOLUNTARY VARIATIONAL INEQUALITIES AND IMPROVED PROJECTION METHOD FOR PROJECTED DYNAMICAL SYSTEM

2021 ◽  
Vol 9 (2) ◽  
pp. 18-24
Author(s):  
Siddharth Mitra ◽  
Prasanta Kumar Das
Keyword(s):  
Dynamical System ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Gradient Method ◽  
Initial Value Problem ◽  
Equivalence Theorem ◽  
Variational Inequality Problems ◽  
Initial Value ◽  
Type Method ◽  
The Given

Purpose of study: To introduce the concept of projective and involuntary variational inequality problems of order  and  respectively. To study the equivalence theorem between these problems. To study the projected dynamical system using self involutory variational inequality problems. Methodology: Improved extra gradient method is used. Main Finding: Using a self-solvable improved extra gradient method we solve the variational inequalities. The algorithm of the projected dynamical system is provided using the RK-4 method whose equilibrium point solves the involutory variational inequality problems. Application of this study: Runge-Kutta type method of order 2 and 4 is used for the initial value problem with the given projected dynamical system with the help of self involutory variational inequality problems. The originality of this study:  The concept of self involutory variational inequality problems, projective and involuntary variational inequality problems of order  and  respectively are newly defined.

scholarly journals Iterative algorithm for singularities of inclusion problems in Hadamard manifolds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Parin Chaipunya ◽  
Konrawut Khammahawong ◽  
Poom Kumam
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Convex Minimization ◽  
Variational Inequality Problems ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Numerical Example ◽  
Minimization Problems ◽  
Convex Minimization Problems

AbstractThe main purpose of this paper is to introduce a new iterative algorithm to solve inclusion problems in Hadamard manifolds. Moreover, applications to convex minimization problems and variational inequality problems are studied. A numerical example also is presented to support our main theorem.

scholarly journals New Tseng’s extragradient methods for pseudomonotone variational inequality problems in Hadamard manifolds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Konrawut Khammahawong ◽  
Poom Kumam ◽  
Parin Chaipunya ◽  
Somyot Plubtieng
Keyword(s):  
Variational Inequality ◽  
Numerical Experiments ◽  
Vector Fields ◽  
Variational Inequality Problem ◽  
Variational Inequality Problems ◽  
Hadamard Manifolds ◽  
Extragradient Methods ◽  
Continuous Vector ◽  
Inequality Problem ◽  
Lipschitz Continuous

AbstractWe propose Tseng’s extragradient methods for finding a solution of variational inequality problems associated with pseudomonotone vector fields in Hadamard manifolds. Under standard assumptions such as pseudomonotone and Lipschitz continuous vector fields, we prove that any sequence generated by the proposed methods converges to a solution of variational inequality problem, whenever it exits. Moreover, we give some numerical experiments to illustrate our main results.

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