### 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 language | English (US) |
---|---|

Pages (from-to) | 46-70 |

Number of pages | 25 |

Journal | ACM Transactions on Mathematical Software |

Volume | 18 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1992 |

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### 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.

Research output: Contribution to journal › Article

*ACM Transactions on Mathematical Software*, vol. 18, no. 1, pp. 46-70. https://doi.org/10.1145/128745.150973

}

TY - JOUR

T1 - TNPACK - a truncated Newton minimization package for large-scale problems

T2 - I. Algorithm and usage

AU - Schlick, Tamar

AU - Fogelson, Aaron

PY - 1992/3

Y1 - 1992/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0026824139&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026824139&partnerID=8YFLogxK

U2 - 10.1145/128745.150973

DO - 10.1145/128745.150973

M3 - Article

VL - 18

SP - 46

EP - 70

JO - ACM Transactions on Mathematical Software

JF - ACM Transactions on Mathematical Software

SN - 0098-3500

IS - 1

ER -