About efficient quasi-newtonian schemes for variational calculations in nuclear structure

The Broyden-Fletcher-Goldhaber-Shanno (BFGS) quasi-newtonian scheme is known as the most efficient scheme for variational calculations of energies. This scheme is actually a member of a one-parameter family of variational methods, known as the Broyden $\beta$-family. In some applications to light nuclei using microscopically derived effective hamiltonians starting from accurate nucleon-nucleon potentials, we actually found other members of the same family which have better performance than the BFGS method. We also extend the Broyden $\beta$-family of algorithms to a two-parameter family of rank three updates which has even better performances.