Extragradient algorithms for equilibrium problems and symmetric generalized hybrid mappings

Weak convergence theorems for symmetric generalized hybrid mappings and equilibrium problems

“…Motivated by these facts and recent works [22,36,6], in this paper, we combine Ishikawa's algorithm with solution methods for equilibrium problems for finding a common element of the set of fixed points of a generalized hybrid mapping and the set of solutions of an equilibrium problem in a real Hilbert space in which the mapping T is symmetric generalized hybrid, and the bifunction f is monotone on C or pseudomonotone on C with respect to its solution set. More precisely, we propose to use the Ishikawa's algorithm for finding a fixed point of the mapping T by incorporating it with the proximal point algorithm and the extragradient algorithms with or without linesearch [20] for solving the equilibrium problem EP(C, f ) (see also [7,8,10,19,32] for more details on the extragradient algorithms).…”

“…To compare with algorithms proposed in [6], we also report the results computed with Algorithm 1 and Algorithm 2 in [6] for this problem with this data and a tolerance = 10 −3 .…”

“…The computation results on Algorithm 2 and Algorithm 3 are reported in Table 1 and Table 2, and the results on Algorithm 1 and Algorithm 2 in [6] are reported in Table 3 and Table 4, respectively, where N.P: the number of the tested problems; Average Times: the average CPU-computation times (in second); Average Iteration: the average number of iterations.…”

Shrinking Extragradient Method for Pseudomonotone Equilibrium Problems and Quasi-Nonexpansive Mappings

“…See, for instance, [8,11,[18][19][20][21][22][23] and the references therein. In 2016, by using both hybrid and extragradient methods together in combination with Ishikawa's iteration concept, Dinh and Kim [24] proposed the following iteration method for finding a common element of fixed points of a symmetric generalized hybrid mapping T and the set of solutions of the equilibrium problem, when a bifunction f is pseudomonotone and Lipschitz-type continuous with positive constants L 1 and L 2 :…”

Extragradient subgradient methods for solving bilevel equilibrium problems

“…In 2008, Tran et al [25] proposed the extragradient algorithm for solving the equilibrium problem by using the strongly convex minimization problem to solve at each iteration. Furthermore, Hieu [9] introduced subgradient extragradient methods for pseudomonotone equilibrium problem and the other methods (see the details in [1, 8, 10, 15, 17, 22, 28]).…”