Hybrid inertial subgradient extragradient methods for variational inequalities and fixed point problems involving asymptotically nonexpansive mappings

Ceng, Lu-Chuan; Shang, Meijuan

doi:10.1080/02331934.2019.1647203

Cited by 70 publications

(41 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We denote by S the solution set of problem (4). Recently, some methods and techniques have been generalized from Euclidean spaces to Riemannian manifolds because the generalization has some important advantages; see, e.g., [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Parallel Tseng’s Extragradient Methods for Solving Systems of Variational Inequalities on Hadamard Manifolds

2019

Self Cite

View full text Add to dashboard Cite

The aim of this article is to study two efficient parallel algorithms for obtaining a solution to a system of monotone variational inequalities (SVI) on Hadamard manifolds. The parallel algorithms are inspired by Tseng’s extragradient techniques with new step sizes, which are established without the knowledge of the Lipschitz constants of the operators and line-search. Under the monotonicity assumptions regarding the underlying vector fields, one proves that the sequences generated by the methods converge to a solution of the monotone SVI whenever it exists.

show abstract

Section: Introductionmentioning

confidence: 99%

Parallel Tseng’s Extragradient Methods for Solving Systems of Variational Inequalities on Hadamard Manifolds

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…Under mild assumptions, they proved that the sequences generated by the proposed algorithms are weakly convergent to a point in Fix(T) ∩ VI(C, A). Recently, gradient-like methods have been studied extensively by many authors; see, e.g., [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”

Section: Algorithmmentioning

confidence: 99%

Inertial-Like Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Asymptotically Nonexpansive and Strictly Pseudocontractive Mappings

et al. 2019

Self Cite

View full text Add to dashboard Cite

Let VIP indicate the variational inequality problem with Lipschitzian and pseudomonotone operator and let CFPP denote the common fixed-point problem of an asymptotically nonexpansive mapping and a strictly pseudocontractive mapping in a real Hilbert space. Our object in this article is to establish strong convergence results for solving the VIP and CFPP by utilizing an inertial-like gradient-like extragradient method with line-search process. Via suitable assumptions, it is shown that the sequences generated by such a method converge strongly to a common solution of the VIP and CFPP, which also solves a hierarchical variational inequality (HVI).

show abstract

“…If VI(C, A) = ∅, one knows that this method has only weak convergence, and only requires that A is monotone and L-Lipschitzian. The literature on the VIP is vast, and Korpelevich's extragradient method has received great attention from many authors, who improved it via various approaches so that some new iterative methods happen to solve the VIP and related optimization problems; see, e.g., [2][3][4][5][6][7][8][9][10][11][12] and the references therein, to name but a few.…”

Section: Introductionmentioning

confidence: 99%

Mann-Type Inertial Subgradient Extragradient Rules for Variational Inequalities and Common Fixed Points of Nonexpansive and Quasi-Nonexpansive Mappings

Ceng

Yao

2021

Axioms

Self Cite

View full text Add to dashboard Cite

Suppose that in a real Hilbert space H, the variational inequality problem with Lipschitzian and pseudomonotone mapping A and the common fixed-point problem of a finite family of nonexpansive mappings and a quasi-nonexpansive mapping with a demiclosedness property are represented by the notations VIP and CFPP, respectively. In this article, we suggest two Mann-type inertial subgradient extragradient iterations for finding a common solution of the VIP and CFPP. Our iterative schemes require only calculating one projection onto the feasible set for every iteration, and the strong convergence theorems are established without the assumption of sequentially weak continuity for A. Finally, in order to support the applicability and implementability of our algorithms, we make use of our main results to solve the VIP and CFPP in two illustrating examples.

show abstract

Hybrid inertial subgradient extragradient methods for variational inequalities and fixed point problems involving asymptotically nonexpansive mappings

Cited by 70 publications

References 28 publications

Parallel Tseng’s Extragradient Methods for Solving Systems of Variational Inequalities on Hadamard Manifolds

Parallel Tseng’s Extragradient Methods for Solving Systems of Variational Inequalities on Hadamard Manifolds

Inertial-Like Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Asymptotically Nonexpansive and Strictly Pseudocontractive Mappings

Mann-Type Inertial Subgradient Extragradient Rules for Variational Inequalities and Common Fixed Points of Nonexpansive and Quasi-Nonexpansive Mappings

Contact Info

Product

Resources

About