Extragradient Methods for Pseudomonotone Variational Inequalities

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Transit assignment: Approach-based formulation, extragradient method, and paradox (2014, methodology): “To speed up the computation process, different rules for updating stepsizes have been proposed (He and Liao, 2002; Noor, 2003; Panicucci et al., 2007).”
Auxiliary Principle Technique for Equilibrium Problems (2004, background): “Adding ( 22 ), (23), and rearranging terms, we have”
An approximate proximal-extragradient type method for monotone variational inequalities (2004, methodology): “Note that the technique developed in [7] an d then extended for pseudo-m onotone variational inequalitie in [10] is useful in following analysis.”
Extragradient algorithms extended to equilibrium problems (2008, methodology): “To overcome this drawback, the extragradient method, first introduced by Korpelevich [15] for finding saddle points, is used to solve monotone, even pseudomonotone, variational inequalities [9,23,24].”
Iterative Schemes for Nonconvex Variational Inequalities (2004, methodology): “Let ^ u be a cluster point of the sequence fung and let the subsequence fujg of the sequence fung converge to ^ u 2 K. Replacing un by unj in (5), taking the limit nj �! 1 , and using ( 12 ), we have”
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].”