In this talk, we begin by reviewing some classical techniques in constrained finite dimensional optimization, which allow to obtain error bounds for the central path of a logarithmic barrier approximation. Next, we apply these ideas to extend such bounds for linear quadratic (deterministic) optimal control problems. After recalling the stochastic minimum principle, we provide natural extensions of the above error estimates for an interior penalty approximation of a linear quadratic stochastic optimal control problem whith non-negativity control constraints. This is a joint work with F. Bonnans from Inria Saclay, Ecole Polytechnique, France.