The Tseng's Extragradient Method for Quasimonotone Variational Inequalities

Nopparat Wairojjana, Nuttapol Pakkaranang, Wachirapong Jirakitpuwapat, Nattawut Pholasa

Abstract

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'sextragradient method and uses a simple self-adaptive step size rule that is independent of the Lipschitz constant. We established a weak convergence theoremfor our method without involving any additional projections or knowledge of theLipschitz constant of a mapping. Finally, we present some numerical experimentsthat show the efficiency and advantage of the proposed method.