In rstan the optimizing function returns a point estiamte from the joint posterior. By default, this uses the L-BFGS algorithm to maximise the posterior. Iterations are terminated when one of three tolerances are met, i.e., the step-size, change of objective function, or norm of the gradient is small enough.

PRO-TIP In the optimisation, the Jacobian adjustment is turned off (since it is unneccessary). In some cases, removing constraints on parameters can improve the performance of the optimiser. When in doubt, try both specifications.

In rstan-2.19.2 the vb command which uses variational inference is still considered experimental.