Extragradient algorithms extended to equilibrium problems

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New extragradient method for a class of equilibrium problems in Hilbert spaces (2018, methodology): “In Euclidean spaces, the extragradient method [22,23] generates two sequences {xn} and { yn } defined by { yn = argmin { λf (xn, y)+ G(xn, y) : y ∈ C } , xn+1 = argmin { λf (yn, y)+ G(xn, y) : y ∈ C } , where x0 ∈ C, G(x, y) is the Bregman distance function and λ is a suitable fixed parameter.”
Parallel Extragradient-Proximal Methods for Split Equilibrium Problems (2015, methodology): “The advantages of the extragradient method are that it is used fo r the class of pseudomonotone bifunctions and two optimization programs are solved at eac h iteration which seems to be numerically easier than the non-linear inequality in the pr oximal method, see for instance [22,25,26] and the ref”
On extragradient-viscosity methods for solving equilibrium and fixed point problems in a Hilbert space (2015, methodology): “If f satisfies properties (A1)–(A4), then the solution set E( f, C) of the equilibrium problem is closed and convex (see [31,33]).”
An inexact subgradient algorithm for Equilibrium Problems (2011, methodology): “3 shows the computational time of IPSM versus our implementation of the Extragradient method given in [21], where a constrained optimization problem, a line search and a projection, have been performed at each iteration.”