Efficient implementation of the truncated-newton algorithm for large-scale chemistry applications

Dexuan Xie, Tamar Schlick

Research output: Contribution to journalArticle

Abstract

To efficiently implement the truncated-Newton (TN) optimization method for large-scale highly nonlinear functions in chemistry, an unconventional modified Cholesky (UMC) factorization is proposed to avoid large modifications 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 modified Cholesky factorizations are found to increase the number of total iterations, as well as computational time, significantly. Since the UMC may generate 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 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 indefinite preconditioner works much better than the minimizer without preconditioning or other minimizers available in the molecular mechanics 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.

Original languageEnglish (US)
Pages (from-to)132-154
Number of pages23
JournalSIAM Journal on Optimization
Volume10
Issue number1
StatePublished - 1999

Fingerprint

Cholesky
Newton-Raphson method
Truncated Newton Method
Efficient Implementation
Factorization
Preconditioner
Chemistry
Cholesky factorisation
Preconditioning
Descent
Minimizer
Molecular mechanics
Potential energy
Limited Memory Method
BFGS Method
Molecular Mechanics
Negative Curvature
Local Minima
Data storage equipment
Nonlinear Function

Keywords

  • Descent direction
  • Indefinite preconditioner
  • Modified Cholesky factorization
  • Molecular potential minimization
  • Truncated-Newton method
  • Unconventional modified Cholesky factorization

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Efficient implementation of the truncated-newton algorithm for large-scale chemistry applications. / Xie, Dexuan; Schlick, Tamar.

In: SIAM Journal on Optimization, Vol. 10, No. 1, 1999, p. 132-154.

Research output: Contribution to journalArticle

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