Strongly convergent inertial forward-backward-forward algorithm without on-line rule for variational inequalities

Abstract

This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces. In our convergence analysis, we do not assume the on-line rule of the inertial parameters and the iterates, which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem. Consequently, our proof arguments are different from what is obtainable in the relevant literature. Finally, we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.