Convergence of One-Step Projected Gradient Methods for Variational Inequalities

On a modified extragradient method for variational inequality problem with application to industrial electricity production

“…Using the Armijo type linesearch procedure and projected reflected gradient method (which is a modification of extragradient method), weak convergence results have recently been obtained in infinite dimensional real Hilbert spaces. For more on the these weak convergence results, please see [32,33]. Observe that in these results (see Theorem 3.1 of [32] and Theorem 4.4 of [33]), A is monotone and L-Lipschitz continuous but the Lipschitz constant L is not needed as an input parameter in their methods.…”

“…For more on the these weak convergence results, please see [32,33]. Observe that in these results (see Theorem 3.1 of [32] and Theorem 4.4 of [33]), A is monotone and L-Lipschitz continuous but the Lipschitz constant L is not needed as an input parameter in their methods.…”

A Projection Algorithm for Non-Monotone Variational Inequalities

“…In the point-to-point case, continuity of T , as well as S * = ∅ are standard assumptions for analyzing (1), (see e.g. [5,29,30,37]). In view of its wide range of applications, it is imperative to consider general versions of (1), which relax the standard assumptions mentioned above.…”

Iterative Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Pseudocontractive Operators

“…Korpelevich's algorithm (4) provides an important idea for solving monotone variational inequality. Please refer to the references [24][25][26][27] for several important extended version of Korpelevich's algorithm.…”