Stochastic PDEs via convex minimization

We prove the applicability of the Weighted Energy-Dissipation (WED)variational principle to nonlinear parabolic stochastic partial differentialequations in abstract form. The WED principle consists in theminimization of a parameter-dependent convex functional on entiretrajectories. Its unique minimizers correspond to elliptic-in-time regularizationsof the stochastic differential problem. As the regularizationparameter tends to zero, solutions of the limiting problem are recovered.This in particular provides a direct approach via convex optimizationto the approximation of nonlinear stochastic partialdifferential equations.