  We study monotone variational inequalities that can arise as optimality
conditions for constrained convex optimisation or convex-concave minimax
problems and propose a novel algorithm that uses only one gradient/operator
evaluation and one projection onto the constraint set per iteration. The
algorithm, which we call fOGDA-VI, achieves a $o \left( \frac{1}{k} \right)$
rate of convergence in terms of the restricted gap function as well as the
natural residual for the last iterate. Moreover, we provide a convergence
guarantee for the sequence of iterates to a solution of the variational
inequality. These are the best theoretical convergence results for numerical
methods for (only) monotone variational inequalities reported in the
literature. To empirically validate our algorithm we investigate a two-player
matrix game with mixed strategies of the two players. Concluding, we show
promising results regarding the application of fOGDA-VI to the training of
generative adversarial nets.
