Characterizations of Levitin–Polyak well-posedness by perturbations for the split variational inequality problem

Optimization ◽  
2016 ◽  
Vol 65 (9) ◽  
pp. 1717-1732 ◽  
Author(s):  
Rong Hu ◽  
Ya-Ping Fang
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Well Posedness ◽  
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.

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.

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