A Modified Tseng's Algorithm with Extrapolation from the Past for Pseudo-monotone Variational Inequalities

Abstract

We present Tseng's forward-backward-forward method with extrapolation from the past for pseudo-monotone variational inequalities in Hilbert spaces. In addition, we propose a variable stepsize scheme of the extrapolated Tseng's algorithm governed by the operator which is pseudo-monotone, Lipschitz continuous and sequentially weak-to-weak continuous. We also investigate the algorithm's adaptive stepsize scenario, which arises when it is impossible to calculate the Lipschitz constant of a pseudo-monotone operator correctly. Finally, we prove a weak convergence theorem and conduct a numerical experiment to support it.