### Abstract

A new method is proposed for finding all maxima and minima of a multivariable function f in a box X
^{(0)}. In this method, the maxima and the minima are calculated by dividing X
^{(0)} into subrogions recursively and bounding the ranges of f in the each subregion applying affine arithmetic and discarding the subrogions which don't possess the possibility of including the point that the maximum (minimum) value occurs. Moreover, to discard more subrogions in initial stage, i.e. to speed the new method, two algorithms are introduced. And to show the efficiency of the new method, some numerical examples are implemented.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science |

Editors | Z. Li, L. Vulkov, J. Wasniewski |

Pages | 424-431 |

Number of pages | 8 |

Volume | 3401 |

Publication status | Published - 2005 |

Event | Third International Conference on Numerical Analysis and Its Applications, NAA 2004 - Rousse, Bulgaria Duration: 2004 Jun 29 → 2004 Jul 3 |

### Other

Other | Third International Conference on Numerical Analysis and Its Applications, NAA 2004 |
---|---|

Country | Bulgaria |

City | Rousse |

Period | 04/6/29 → 04/7/3 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science (miscellaneous)

### Cite this

*Lecture Notes in Computer Science*(Vol. 3401, pp. 424-431)

**A method which finds the maxima and minima of a multivariable function applying affine arithmetic.** / Miyajima, Shinya; Kashiwagi, Masahide.

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

*Lecture Notes in Computer Science.*vol. 3401, pp. 424-431, Third International Conference on Numerical Analysis and Its Applications, NAA 2004, Rousse, Bulgaria, 04/6/29.

}

TY - GEN

T1 - A method which finds the maxima and minima of a multivariable function applying affine arithmetic

AU - Miyajima, Shinya

AU - Kashiwagi, Masahide

PY - 2005

Y1 - 2005

N2 - A new method is proposed for finding all maxima and minima of a multivariable function f in a box X (0). In this method, the maxima and the minima are calculated by dividing X (0) into subrogions recursively and bounding the ranges of f in the each subregion applying affine arithmetic and discarding the subrogions which don't possess the possibility of including the point that the maximum (minimum) value occurs. Moreover, to discard more subrogions in initial stage, i.e. to speed the new method, two algorithms are introduced. And to show the efficiency of the new method, some numerical examples are implemented.

AB - A new method is proposed for finding all maxima and minima of a multivariable function f in a box X (0). In this method, the maxima and the minima are calculated by dividing X (0) into subrogions recursively and bounding the ranges of f in the each subregion applying affine arithmetic and discarding the subrogions which don't possess the possibility of including the point that the maximum (minimum) value occurs. Moreover, to discard more subrogions in initial stage, i.e. to speed the new method, two algorithms are introduced. And to show the efficiency of the new method, some numerical examples are implemented.

UR - http://www.scopus.com/inward/record.url?scp=24144465149&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24144465149&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:24144465149

VL - 3401

SP - 424

EP - 431

BT - Lecture Notes in Computer Science

A2 - Li, Z.

A2 - Vulkov, L.

A2 - Wasniewski, J.

ER -