### 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 language | English (US) |
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Pages (from-to) | 71-111 |

Number of pages | 41 |

Journal | ACM Transactions on Mathematical Software |

Volume | 18 |

Issue number | 1 |

DOIs | |

Publication status | 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