Stan provides optimization algorithms which find modes of the density specified by a Stan program. Such modes may be used as parameter estimates or as the basis of approximations to a Bayesian posterior.
Stan provides three different optimizers, a Newton optimizer, and two related quasi-Newton algorithms, BFGS and L-BFGS; see Nocedal and Wright (2006) for thorough description and analysis of all of these algorithms. The L-BFGS algorithm is the default optimizer. Newton’s method is the least efficient of the three, but has the advantage of setting its own stepsize.