TNPACK - a truncated Newton minimization package for large-scale problems

I. Algorithm and usage

Tamar Schlick, Aaron Fogelson

Research output: Contribution to journalArticle

Abstract

We present a FORTRAN package of subprograms for minimizing multivariate functions without constraints by a truncated Newton algorithm. The algorithm is especially suited for problems involving a large number of variables. Truncated Newton methods allow approximate, rather than exact, solutions to the Newton equations. Truncation is accomplished in the present version by using the preconditioned Conjugate Gradient algorithm (PCG) to solve approximately the Newton equations. The preconditioner M is factored in PCG using a sparse modified Cholesky factorization based on the Yale Sparse Matrix Package. In this paper we briefly describe the method and provide details for program usage.

Original languageEnglish (US)
Pages (from-to)46-70
Number of pages25
JournalACM Transactions on Mathematical Software
Volume18
Issue number1
DOIs
StatePublished - Mar 1992

Fingerprint

Preconditioned Conjugate Gradient
Conjugate Gradient Algorithm
Large-scale Problems
D.3.2 [Programming Languages]: Language Classifications - Fortran
Truncated Newton Method
Cholesky factorisation
Multivariate Functions
Sparse matrix
Truncation
Preconditioner
Exact Solution
FORTRAN (programming language)
Newton-Raphson method
Factorization

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Safety, Risk, Reliability and Quality
  • Applied Mathematics

Cite this

TNPACK - a truncated Newton minimization package for large-scale problems : I. Algorithm and usage. / Schlick, Tamar; Fogelson, Aaron.

In: ACM Transactions on Mathematical Software, Vol. 18, No. 1, 03.1992, p. 46-70.

Research output: Contribution to journalArticle

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