Douglas-Rachford splitting method for nonconvex stochastic optimal control

Motivated by the numerical resolution of stochastic optimal control problems, particularly those involving nonlinear dynamics, we investigate the convergence properties of the Douglas-Rachford splitting algorithm in a nonconvex and infinite-dimensional setting. We introduce an extension of the method that applies when one component of the objective function is continuously differentiable with a locally Lipschitz gradient, while the other is weakly lower semicontinuous with a bounded domain.