Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space

By Yair Censor, Aviv Gibali, Simeon Reich. Optim. Methods Softw., 2011

448 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ed3723a62f3545b4be2ef36d6f93d9867cfb8aeb

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

An efficient iterative method for finding common fixed point and variational inequalities in Hilbert spaces (2018, methodology): “[15,34,35] for VIs and of Kraikaew and Saejung [28] for (4) in which only one projection onto the feasible set C is executed per each iteration.”
Modified subgradient extragradient algorithms for variational inequality problems and fixed point problems (2018, methodology): “In order to obtain the strong convergence, these authors also introduced in [4] the following hybrid algorithm, ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎪⎪⎩ x0 ∈ H yn = PC(xn − μAxn), Tn = {x ∈ H : 〈xn − μAxn − yn, x − yn〉 ≤ 0}, zn = αnxn + (1 − αn)PTn(xn − μAyn), Cn = {w ∈ H : ‖zn − w‖ ≤ ‖xn − w‖}, Qn = {w ∈ H : 〈xn − w, ”
Iterative algorithm with self-adaptive step size for approximating the common solution of variational inequality and fixed point problems (2021, methodology): “In [12], they proved that Algorithm (3) converges weakly to an element in VI(C,A) = ∅.”
Fast and Simple Bregman Projection Methods for Solving Variational Inequalities and Related Problems in Banach Spaces (2020, background): “There exist many generalizations/modifications of the SEM which try to tackle these issues, for example, see [8,9,20,23]).”
Modified Tseng's extragradient methods for solving pseudo-monotone variational inequalities (2019, methodology): “This method converges for pseudo-monotone VIs in finite dimensional Euclidean spaces [8] and monotone VIs in infinite dimensional Hilbert spaces [6,7].”
Single projection method for pseudo-monotone variational inequality in Hilbert spaces (2018, unknown): “[10] were the first to prove strong convergence result for VI(A,C) (1) with a monotone and L-Lipschitz-continuous mapping A using essentially only one projection onto C using this method: x1 ∈ H; yn = PC(xn − λnAxn), Tn := {w ∈ H : 〈xn − λnAxn − yn,w− yn〉 ≤ 0}, zn = αnxn + (1− αn)PTn(xn − λnAyn), Cn”
Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces (2014, methodology): “The same authors continued the study of this method in [15, 16].”