Efficient Implementation of the Truncated-Newton Algorithm for Large-Scale Chemistry Applications

To e ciently implement the truncated-Newton (TN) optimization method for largescale, highly nonlinear functions in chemistry, an unconventional modi ed Cholesky (UMC) factorization is proposed to avoid large modi cations to a problem-derived preconditioner, used in the inner loop in approximating the TN search vector at each step. The main motivation is to reduce the computational time of the overall method: large changes in standard modi ed Cholesky factorizations are found to increase the number of total iterations, as well as computational time, signi cantly. Since the UMC may generate an inde nite, rather than a positive de nite, e ective preconditioner, we prove that directions of descent still result. Hence, convergence to a local minimum can be shown, as in classic TN methods, for our UMC-based algorithm. Our incorporation of the UMC also requires changes in the TN inner loop regarding the negative-curvature test (which we replace by a descent direction test) and the choice of exit directions. Numerical experiments demonstrate that the unconventional use of an inde nite preconditioner works much better than the minimizer without preconditioning or other minimizers available in the molecular mechanics and dynamics package CHARMM. Good performance of the resulting TN method for large potential energy problems is also shown with respect to the limited-memory BFGS method, tested both with and without preconditioning.