This paper introduces a projection and contraction algorithm with extrapolation from the past for solving variational inequalities in Hilbert spaces. The proposed method reduces the number of operator evaluations per iteration from two to one by reusing past iterations. Under standard assumptions, we prove strong convergence of the generated sequence. Numerical experiments on solving large-scale Harker-Pang problems demonstrate its superior efficiency and robustness compared to several well-established methods.
Citation
Y. Shehu, J. Bai*, A strongly convergent projection and contraction algorithm with extrapolations from the past, Communications in Nonlinear Science and Numerical Simulation，In press, (2026)