Algorithms for Systems of Nonlinear Variational Inequalities

Cho, Yeol Je; Fang, Ya-Ping; Huang, Nan-jing; Hwang, Ho Jin

doi:10.4134/jkms.2004.41.3.489

Cited by 53 publications

(45 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above nonlinear variational inequality problem was studied by Cho et al [4]. Case (III): If M 1 (x) = ∂δ K1 (x) and M 2 (y) = ∂δ K2 (y) for all x ∈ K 1 and y ∈ K 2 , where K 1 and K 2 are nonempty closed convex subsets of X 1 and X 2 , respectively, and δ K1 and δ K2 are indicator functions of K 1 and K 2 , respectively.…”

Section: System Of Nonlinear Variational Inclusion Problemsmentioning

confidence: 99%

System of nonlinear variational inclusion problems with $(A,\eta)$-maximal monotonicity in Banach spaces

Sahu

Mahato

Mohapatra

2017

Stat., optim. inf. comput.

View full text Add to dashboard Cite

This paper deals with a new system of nonlinear variational inclusion problems involving (A, η)-maximal relaxed monotone and relative (A, η)-maximal monotone mappings in 2-uniformly smooth Banach spaces. Using the generalized resolvent operator technique, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also proved for other system of variational inclusion problems involving relative (A, η)-maximal monotone mappings and (H, η)-maximal monotone mappings.

show abstract

Section: System Of Nonlinear Variational Inclusion Problemsmentioning

confidence: 99%

System of nonlinear variational inclusion problems with $(A,\eta)$-maximal monotonicity in Banach spaces

Sahu

Mahato

Mohapatra

2017

Stat., optim. inf. comput.

View full text Add to dashboard Cite

show abstract

“…Subsequently, the most nature, direct, simple and efficient framework for general treatment of wide range of problems are provided for the variational inequalities. Roughly speaking, many researchers interest to develop several numerical methods for solving variational inequalities and relaxed optimization problems(see [2,10,11,12,13,33,34,35,36] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Existence and convergence theorems for the split quasi variational inequality problems on proximally smooth sets

Tangkhawiwetkul¹,

Petrot²

2016

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

In this paper, we consider the split quasi variational inequality problems over a class of nonconvex sets, as uniformly prox-regular sets. The sufficient conditions for the existence of solutions of such a problem are provided. Furthermore, an iterative algorithm for finding a solution is constructed and its convergence analysis are considered. The results in this paper improve and extend the variational inequality problems which have been appeared in literature.

show abstract

“…Inspired and motivated by recent research works in this field, see [1,2,7,8,13,14,15,17,21,25], we introduce a new system of generalized nonlinear mixed variational inclusions and suggest an iterative algorithm. By the definition of relaxed cocoersive mapping and resolvent operator techniques, we find 384 BYUNG-SOO LEE AND SALAHUDDIN the exact solutions of our systems of generalized nonlinear mixed variational inclusions involving different nonlinear operators and fixed point problems in Hilbert spaces.…”

Section: Introductionmentioning

confidence: 99%

System of Generalized Nonlinear Mixed Variational Inclusions Involving Relaxed Cocoercive Mappings in Hilbert Spaces

Lee¹,

Salahuddin²

2015

East Asian mathematical journal

View full text Add to dashboard Cite

Abstract. We considered a new system of generalized nonlinear mixed variational inclusions in Hilbert spaces and define an iterative method for finding the approximate solutions of this class of system of generalized nonlinear mixed variational inclusions. We also established that the approximate solutions obtained by our algorithm converges to the exact solutions of a new system of generalized nonlinear mixed variational inclusions.

show abstract

Algorithms for Systems of Nonlinear Variational Inequalities

Cited by 53 publications

References 6 publications

System of nonlinear variational inclusion problems with $(A,\eta)$-maximal monotonicity in Banach spaces

System of nonlinear variational inclusion problems with $(A,\eta)$-maximal monotonicity in Banach spaces

Existence and convergence theorems for the split quasi variational inequality problems on proximally smooth sets

System of Generalized Nonlinear Mixed Variational Inclusions Involving Relaxed Cocoercive Mappings in Hilbert Spaces

Contact Info

Product

Resources

About