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

Pages (from-to) | 141 |

Number of pages | 1 |

Journal | ACM Transactions on Mathematical Software |

Volume | 18 |

Issue number | 2 |

DOIs | |

State | Published - Jan 6 1992 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*ACM Transactions on Mathematical Software*, vol. 18, no. 2, pp. 141. https://doi.org/10.1145/146847.146921

}

TY - JOUR

T1 - Algorithm 702

T2 - TNPACK–A Truncated Newton Minimization Package for Large-Scale Problems: I. Algorithm and Usage

AU - Schlick, Tamar

AU - Fogelson, Aaron

PY - 1992/1/6

Y1 - 1992/1/6

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 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.

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 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.

KW - nonlinear optimization

KW - preconditioned conjugate gradient

KW - sparse matrices

KW - truncated Newton methods

UR - http://www.scopus.com/inward/record.url?scp=84976848878&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976848878&partnerID=8YFLogxK

U2 - 10.1145/146847.146921

DO - 10.1145/146847.146921

M3 - Article

AN - SCOPUS:0026870308

VL - 18

SP - 141

JO - ACM Transactions on Mathematical Software

JF - ACM Transactions on Mathematical Software

SN - 0098-3500

IS - 2

ER -