Efficient implementation of the truncated-Newton algorithm for large-scalechemistry applications

To efficiently implement the truncated-Newton (TN) optimization method for large-scale, highly nonlinear functions in chemistry, an unconventional mod ified Cholesky (UMC) factorization is proposed to avoid large modifications to a problem-derived preconditioner, used in the inner loop in approximati ng the TN search vector at each step. The main motivation is to reduce the computational time of the overall method: large changes in standard modifie d Cholesky factorizations are found to increase the number of total iterati ons, as well as computational time, significantly. Since the UMC may genera te an indefinite, rather than a positive definite, effective 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 al gorithm. 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 de monstrate that the unconventional use of an indefinite preconditioner works much better than the minimizer without preconditioning or other minimizers available in the molecular mechanics package CHARMM. Good performance of t he resulting TN method for large potential energy problems is also shown wi th respect to the limited-memory BFGS method, tested both with and without preconditioning.