Computing families of periodic orbits through optimization methods

The techniques used for the numerical computation of families of periodic o rbits of dynamical systems are based on predictor-corrector schemes. These schemes usually depend on solving systems of approximate equations involvin g the solutions of the equations of motion and variation. In this contribut ion we apply some well-known unconstrained optimization methods in obtainin g the solutions of these approximate equations and we compare their efficie ncy on a specific problem of Celestial Mechanics.