New extragradient-type methods for general variational inequalities

By Muhammad Aslam Noor. 2003

115 citations recorded by the source corpus.

In this paper, we consider and analyze a new class of extragradient-type methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is weaker condition than monotonicity. Our proof of convergence is very simple as compared with other methods. The proposed methods include several new and known methods as special cases. Our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems.

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

View Paper: https://www.semanticscholar.org/paper/c6848eb1afd586894d0442e1a97d9893dbc69a50

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

An Efficient Primal-Dual Hybrid Gradient Algorithm For Total Variation Image Restoration (2008, background): “There are many other variants of the original extragradient algorithm with diﬀerent predictor search rule and corrector step size aiming to improve performance (see [15] and [20]).”
Some developments in general variational inequalities (2004, methodology): “For the convergence analysis and applications of three-step splitting methods in variational inequalities and mathematical programming problems, see [13,14,83,86,88,89,93,136].”
Projection algorithms for solving a system of general variational inequalities (2009, methodology): “For the applications and numerical methods, see [10,13–16,22–24] and the references therein.”
Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems (2004, background): “Korpelevich in 1976, (see [7, 8]; for recent results, see [15] and references therein); in particular, she proved the convergence of zt to a solution of the VI.”
Iterative Schemes for Nonconvex Variational Inequalities (2004, background): “From ( 10 ) and (11), we obtain (7), the required result.”
New Trends in General Variational Inequalities (2020, background): “the general variational inequalities, readers are referred to the state-of-art articles of Noor [85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 100, 101, 102, 103, 104, 105, 110, 118, 119, 120, 121, 122, 124] and the references therein.”