  We prove the applicability of the Weighted Energy-Dissipation (WED)
variational principle [50] to nonlinear parabolic stochastic partial
differential equations in abstract form. The WED principle consists in the
minimization of a parameter-dependent convex functional on entire trajectories.
Its unique minimizers correspond to elliptic-in-time regularizations of the
stochastic differential problem. As the regularization parameter tends to zero,
solutions of the limiting problem are recovered. This in particular provides a
direct approch via convex optimization to the approximation of nonlinear
stochastic partial differential equations.
