The Tseng's Extragradient Method for Quasimonotone Variational Inequalities
Nopparat Wairojjana, Nuttapol Pakkaranang, Wachirapong Jirakitpuwapat, Nattawut Pholasa · Thai Journal of Mathematics · 2021
In this paper, we examine the weak convergence of a method to solve classical variational inequalities problems with quasi-monotone and Lipschitz -continuous mapping in real Hilbert space. The proposed method is inspired from Tseng's extragradient method and uses a simple self-adaptive step size rule that is independent of the Lipschitz constant. We established a weak convergence theorem for our method without involving any additional projections or knowledge of the Lipschitz constant of a mapping. Finally, we present some numerical experiments that show the efficiency and advantage of the proposed method.