The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space

By Yair Censor, Aviv Gibali, Simeon Reich. Journal of Optimization Theory and Applications, 2011

926 citations recorded by the source corpus.

We present a subgradient extragradient method for solving variational inequalities in Hilbert space. In addition, we propose a modified version of our algorithm that finds a solution of a variational inequality which is also a fixed point of a given nonexpansive mapping. We establish weak convergence theorems for both algorithms.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2e3f962293bd4720086385a4af4c98c35c30489a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. Yekini Shehu
2. Dang Van Hieu
3. Duong Viet Thong
4. Aviv Gibali
5. Oluwatosin Temitope Mewomo
6. Rapeepan Kraikaew
7. Satit Saejung
8. Lu-Chuan Ceng

In Computational Theory and Mathematics

1. Yekini Shehu
2. Dang Van Hieu
3. Oluwatosin Temitope Mewomo
4. Duong Viet Thong
5. Aviv Gibali
6. Timilehin Opeyemi Alakoya
7. Lateef Olakunle Jolaoso
8. Adeolu Taiwo

In Numerical Analysis

1. Yekini Shehu
2. Oluwatosin Temitope Mewomo
3. Dang Van Hieu
4. Duong Viet Thong
5. Aviv Gibali
6. Timilehin Opeyemi Alakoya
7. Lateef Olakunle Jolaoso
8. Adeolu Taiwo

Citations in the corpus

• Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces (2014, methodology): “2 of [14].”
• Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets (2013, methodology): “This idea is also used by Censor et al. [30] in the subgradient extragradient method for solving variational inequalities in a Hilbert space.”
• Modified subgradient extragradient algorithms for solving monotone variational inequalities (2018, methodology): “[4] for solvingVI(C, F) in real Hilbert space.”
• Advances in Variational and Hemivariational Inequalities (2015, background): “Since u0 is a local minimizer of φλ, as in [7] (see the proof of Theorem 2.”
• A self adaptive inertial subgradient extragradient algorithm for variational inequality and common fixed point of multivalued mappings in Hilbert spaces (2019, methodology): “[13], KraikaewandSaejung [50], Thong andHieu [27]which require that the stepsize satisfies μn = μ ∈ (︂ 0, (1)L )︂ , where L is the Lipschitz constant of A.”