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

II. Implementation examples

Tamar Schlick, Aaron Fogelson

Research output: Contribution to journalArticle

Abstract

We have recently presented a FORTRAN package for solving unconstrained optimization problems by a truncated Newton algorithm. TNPACK is intended to solve problems for which some separability and sparsity-structure information of the Hessian is available. The Newton equations are solved approximately at each step by a Preconditioned Conjugate Gradient method, with adaptations to indefinite systems; the linear system involving the preconditioner is solved by a sparse modified Cholesky factorization based on the Yale Sparse Matrix Package. In this paper we describe implementation examples on two standard optimization problems and two real-life applications. Our intent is to aid users in their own applications, to highlight key options and parameters that may require tailoring to the problem and to describe application areas for which TNPACK is most suited. These examples will illustrate various strategies for formulating preconditioners, applying reorderings to them in order to minimize fill-in, enforcing truncation, and dealing with indefinite regions.

Original languageEnglish (US)
Pages (from-to)71-111
Number of pages41
JournalACM Transactions on Mathematical Software
Volume18
Issue number1
DOIs
StatePublished - Mar 1992

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Large-scale Problems
D.3.2 [Programming Languages]: Language Classifications - Fortran
Preconditioner
Optimization Problem
Indefinite Systems
Cholesky factorisation
Preconditioned Conjugate Gradient Method
Conjugate gradient method
Information Structure
Reordering
Unconstrained Optimization
Separability
Sparse matrix
Factorization
Sparsity
Truncation
Linear systems
Linear Systems
Minimise

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 : II. Implementation examples. / Schlick, Tamar; Fogelson, Aaron.

In: ACM Transactions on Mathematical Software, Vol. 18, No. 1, 03.1992, p. 71-111.

Research output: Contribution to journalArticle

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