### Abstract

Original language | English |
---|---|

Title of host publication | System modeling and optimization |

Subtitle of host publication | proceedings of the 22nd IFIP TC7 Conference held from , July 18-22, 2005, Turin, Italy |

Editors | F. Ceragioli, A. Dontchev, H. Furuta, K. Marti, L. Pandolfi |

Place of Publication | New York |

Publisher | Springer |

Pages | 275-293 |

ISBN (Print) | 9780387327747, 9781441941039 |

DOIs | |

Publication status | Published - 2006 |

### Publication series

Name | IFIP Advances in Information and Communication Technology |
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Publisher | Springer |

Number | 199 |

ISSN (Print) | 1868-4238 |

### Fingerprint

### Keywords

- Nonlinear programming
- Filter
- SQP
- Quasi-Newton
- Symmetric rank one
- Limited memory

### Cite this

*System modeling and optimization: proceedings of the 22nd IFIP TC7 Conference held from , July 18-22, 2005, Turin, Italy*(pp. 275-293). (IFIP Advances in Information and Communication Technology; No. 199). New York: Springer . https://doi.org/10.1007/0-387-33006-2_25

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*System modeling and optimization: proceedings of the 22nd IFIP TC7 Conference held from , July 18-22, 2005, Turin, Italy.*IFIP Advances in Information and Communication Technology, no. 199, Springer , New York, pp. 275-293. https://doi.org/10.1007/0-387-33006-2_25

**A new low-rank quasi-Newton update scheme for nonlinear programming.** / Fletcher, R.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - A new low-rank quasi-Newton update scheme for nonlinear programming

AU - Fletcher, R.

PY - 2006

Y1 - 2006

N2 - A new quasi-Newton scheme for updating a low rank positive semi-definite Hessian approximation is described, primarily for use in sequential quadratic programming methods for nonlinear programming. Where possible the symmetric rank one update formula is used, but when this is not possible a new rank two update is used, which is not in the Broyden family, although invariance under linear transformations of the variables is preserved. The representation provides a limited memory capability, and there is an ordering scheme which enables’ old’ information to be deleted when the memory is full. Hereditary and conjugacy properties are preserved to the maximum extent when minimizing a quadratic function subject to linear constraints. Practical experience is described on small (and some larger) CUTE test problems, and is reasonably encouraging, although there is some evidence of slow convergence on large problems with large null spaces.

AB - A new quasi-Newton scheme for updating a low rank positive semi-definite Hessian approximation is described, primarily for use in sequential quadratic programming methods for nonlinear programming. Where possible the symmetric rank one update formula is used, but when this is not possible a new rank two update is used, which is not in the Broyden family, although invariance under linear transformations of the variables is preserved. The representation provides a limited memory capability, and there is an ordering scheme which enables’ old’ information to be deleted when the memory is full. Hereditary and conjugacy properties are preserved to the maximum extent when minimizing a quadratic function subject to linear constraints. Practical experience is described on small (and some larger) CUTE test problems, and is reasonably encouraging, although there is some evidence of slow convergence on large problems with large null spaces.

KW - Nonlinear programming

KW - Filter

KW - SQP

KW - Quasi-Newton

KW - Symmetric rank one

KW - Limited memory

U2 - 10.1007/0-387-33006-2_25

DO - 10.1007/0-387-33006-2_25

M3 - Chapter

SN - 9780387327747

SN - 9781441941039

T3 - IFIP Advances in Information and Communication Technology

SP - 275

EP - 293

BT - System modeling and optimization

A2 - Ceragioli, F.

A2 - Dontchev, A.

A2 - Furuta, H.

A2 - Marti, K.

A2 - Pandolfi, L.

PB - Springer

CY - New York

ER -