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In infinite-dimensional Hilbert spaces we device a class of stronglyconvergent primal-dual schemes for solving variational inequalities defined bya Lipschitz continuous and pseudomonote map. Our novel numerical scheme isbased on Tseng's forward-backward-forward scheme, which is known to displayweak convergence, unless very strong global monotonicity assumptions are madeon the involved operators. We provide a simple augmentation of this algorithmwhich is computationally cheap and still guarantees strong convergence to aminimal norm solution of the underlying problem. We provide an adaptiveextension of the algorithm, freeing us from requiring knowledge of the globalLipschitz constant. We test the performance of the algorithm in thecomputationally challenging task to find dynamic user equilibria in trafficnetworks and verify that our scheme is at least competitive to state-of-the-artsolvers, and in some case even improve upon them.

Strong Convergence of Forward-Backward-Forward Methods for  Pseudo-monotone Variational Inequalities with Applications to Dynamic User  Equilibrium in Traffic Networks