Algorithm 702: 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 1992 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)141
Number of pages1
JournalACM Transactions on Mathematical Software
Volume18
Issue number2
DOIs
StatePublished - Jan 6 1992

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

Keywords

  • nonlinear optimization
  • preconditioned conjugate gradient
  • sparse matrices
  • truncated Newton methods

ASJC Scopus subject areas

  • Software
  • Applied Mathematics

Cite this

Algorithm 702 : 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. 2, 06.01.1992, p. 141.

Research output: Contribution to journalArticle

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