An Accelerated Popov's Subgradient Extragradient Method for Strongly Pseudomonotone Equilibrium Problems in a Real Hilbert Space With Applications - Wairojjana, Nopparat; Rehman, Habib ur; Pakkaranang, Nuttapol; Khanpanuk, Chainarong (Communications in Mathematics and Applications, 2020)
In this paper, we introduce a subgradient extragradient method to find the numerical solution of strongly pseudomonotone equilibrium problems with the Lipschitz-type condition on a bifunction in a real Hilbert space. The strong convergence theorem for the proposed method is precisely established on the basis of the standard cost bifunction assumptions. The application of our convergence results is also considered in the context of variational inequalities. For numerical analysis, we consider the well-known Nash-Cournot oligopolistic equilibrium model to support our well-established convergence results.
Keywords: Subgradient extragradient method; Strongly pseudomonotone equilibrium problems; Lipschitz-type condition; Strong convergence theorem