Projection algorithms for solving nonmonotone equilibrium problems in Hilbert space

Solving common nonmonotone equilibrium problems using an inertial parallel hybrid algorithm with Armijo line search with applications to image recovery

“…In 2003, Dinh and Kim [11] introduced the projection algorithm with line search of a bifunction which is not required to be pseudomonotone to solve the equilibrium problem. A weak convergence theorem was proved under continuity and convexity assumptions on the bifunction ψ, which is not required to have any monotonicity property, and assuming the solution set of Minty equilibrium problem (1.2) is nonempty.…”

“…After that, many mathematicians have improved it in many ways, see [19,23,26]. In 2018, Iyiola et al [14] motivated the inertial-type algorithms with the algorithm of Dinh and Kim [11], they obtained convergence theorems and presented the following inertial-type iterative method with Armijo line search stepsize which is faster and more efficient than the algorithm by Dinh and Kim [11].…”

Extragradient Method for Fixed Points in CAT(0) Spaces

“…The Armijo-type method for pseudomonotone equilibrium problems was formulated in [6] in the setting of Hilbert spaces. After that, the authors in [7] presented the convergence of weak and strong types for the algorithms in order to solve the equilibrium problem. The admirable outcomes are due to Dinh and Kim in which there is no restriction on monotonicity of the bifunction.…”

A linesearch projection algorithm for solving equilibrium problems without monotonicity in Hilbert spaces

“…However, the pseudomonotonicity assumption may not be satisfied in some pratical problems, for instance, the Nash-Cournot equilibrium problem considered in [30]. In light of this situation, motivated by Dinh and Muu [12] and Ye and He [44], Dinh and Kim [13] proposed projection algorithms for solving nonmonotone EP (f, C). Their convergence does not require any monotonicity and Lipschitz-type property of the equilibrium bifunction f but the nonemptyness of S M .…”