Abstract
This paper presents two inertial extragradient algorithms for finding a solution of split pseudomonotone equilibrium problems in the setting of real Hilbert spaces. The weak and strong convergence theorems of the introduced algorithms are presented under some constraint qualifications of the scalar sequences. The discussions on the numerical experiments are also provided to demonstrate the effectiveness of the proposed algorithms.
Highlights
We introduce Algorithm 1 for solving the split equilibrium problems (11)
We present two algorithms for solving the split equilibrium problems, when the bifunctions are pseudomonotone and Lipschitz-type continuous in the framework of real
Some numerical experiments in which the bifunctions are generated from the Nash–Cournot oligopolistic equilibrium models of electricity markets and the Cournot–Nash models, respectively, are performed to illustrate the convergence of introduced algorithms and compare them with some algorithms
Summary
The equilibrium problem is a problem of finding a point x ∗ ∈ C such that f ( x ∗ , y) ≥ 0, ∀y ∈ C, Seoane-Sepúlveda. In 2019, by using the ideas of inertial and extragradient methods, Vinh and Muu [11] proposed the following method for solving the equilibrium problem, when the bifunction f is pseudomonotone and satisfies Lipschitz-type continuous conditions with positive constants c1 and c2 : x0 , x1 ∈ C,. Under the setting of f : H1 × H1 → R and g : H2 × H2 → R, Kim and Dinh [18] proposed the following the extragradient method for finding a solution of the split equilibrium problems, when the bifunctions f and g are pseudomonotone and satisfy Lipschitz-type continuous conditions with positive constants c1 and c2 : x0 ∈ C, n o yk = arg min λk f ( xk , y) + 12 ky − xk k2 : y ∈ C ,.
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