Inertial methods for finding minimum-norm solutions of the split variational inequality problem beyond monotonicity

2021 ◽  
Author(s):  
G. N. Ogwo ◽  
C. Izuchukwu ◽  
O. T. Mewomo
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Minimum Norm ◽  
Inequality Problem ◽  
Split Variational Inequality ◽  
Split Variational Inequality Problem

scholarly journals A Cyclic Method for Solutions of a Class of Split Variational Inequality Problem in Banach Space

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Bashir Ali ◽  
Aisha A. Adam ◽  
Yusuf Ibrahim
Keyword(s):  
Banach Space ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Variational Inequality Problem ◽  
Strong Convergence Theorem ◽  
Inequality Problem ◽  
Cyclic Algorithm ◽  
Split Variational Inequality ◽  
Split Variational Inequality Problem

In this paper, a cyclic algorithm for approximating a class of split variational inequality problem is introduced and studied in some Banach spaces. A strong convergence theorem is proved. Some applications of the theorem are presented. The results presented here improve, unify, and generalize certain recent results in the literature.

Convergence analysis of an inertial accelerated iterative algorithm for solving split variational inequality problem

2019 ◽  
Vol 10 (4) ◽  
pp. 339-353 ◽  
Author(s):  
Ferdinard U. Ogbuisi ◽  
Oluwatosin T. Mewomo
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Iterative Scheme ◽  
Real Hilbert Space ◽  
Operator Norm ◽  
Step Size ◽  
Inequality Problem ◽  
Convex Minimization Problems ◽  
Split Variational Inequality ◽  
Split Variational Inequality Problem

AbstractIn this paper, we introduce an iterative scheme involving an inertial term and a step size independent of the operator norm for approximating a solution to a split variational inequality problem in a real Hilbert space. Furthermore, we prove a convergence theorem for the sequence generated by the proposed operator norm independent inertial accelerated iterative scheme. We applied our result to solve split convex minimization problems, split zero problem and further give a numerical example to demonstrate the efficiency of the proposed algorithm.

INERTIAL RELAXED TSENG METHOD FOR SOLVING VARIATIONAL INEQUALITY PROBLEM IN HILBERT SPACE

2021 ◽  
Vol 10 (12) ◽  
pp. 3597-3623
Author(s):  
F. Akusah ◽  
A.A. Mebawondu ◽  
H.A. Abass ◽  
M.O. Aibinu ◽  
O.K. Narain
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Numerical Experiments ◽  
Variational Inequality Problem ◽  
Extrapolation Method ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Inequality Problem ◽  
Weaker Conditions

The research efforts of this paper is to present a new inertial relaxed Tseng extrapolation method with weaker conditions for approximating the solution of a variational inequality problem, where the underlying operator is only required to be pseudomonotone. The strongly pseudomonotonicity and inverse strongly monotonicity assumptions which the existing literature used are successfully weakened. The strong convergence of the proposed method to a minimum-norm solution of a variational inequality problem are established. Furthermore, we present an application and some numerical experiments to show the efficiency and applicability of our method in comparison with other methods in the literature.

scholarly journals Split general quasi-variational inequality problem

2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Kaleem Raza Kazmi
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Natural Extension ◽  
Iterative Algorithms ◽  
Variational Inequality Problems ◽  
Convergence Criteria ◽  
Inequality Problem ◽  
Special Cases ◽  
Quasi Variational Inequality ◽  
Split Variational Inequality Problem

AbstractIn this paper, we introduce a split general quasi-variational inequality problem which is a natural extension of a split variational inequality problem, quasivariational and variational inequality problems in Hilbert spaces. Using the projection method, we propose an iterative algorithm for a split general quasi-variational inequality problem and discuss some special cases. Further, we discuss the convergence criteria of these iterative algorithms. The results presented in this paper generalize, unify and improve many previously known results for quasi-variational and variational inequality problems.

scholarly journals Split General Strong Nonlinear Quasi-Variational Inequality Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Yali Zhao ◽  
Dongxue Han
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Variational Inequality Problem ◽  
Natural Extension ◽  
Variational Inequality Problems ◽  
Convergence Criteria ◽  
Inequality Problem ◽  
Strongly Nonlinear ◽  
Quasi Variational Inequality ◽  
Split Variational Inequality Problem

We introduce a split general strong nonlinear quasi-variational inequality problem which is a natural extension of a split general quasi-variational inequality problem, split variational inequality problem, and quasi-variational and variational inequality problems in Hilbert spaces. Using the projection method, we propose an iterative algorithm for the split general strongly nonlinear quasi-variational inequality problem and discuss the convergence criteria of the iterative algorithm. The results presented here generalized, unify, and improve many previously known results for quasi-variational and variational inequality problems.

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