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.
Nocedal, Jorge, and Stephen J. Wright. 2006. Numerical Optimization. Second. Berlin: Springer-Verlag.