### 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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Pages (from-to) | 424-431 |

Number of pages | 8 |

Journal | LECTURE NOTES IN COMPUTER SCIENCE |

Volume | 3401 |

Publication status | Published - 2005 Sep 12 |

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

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Miyajima, S., & Kashiwagi, M. (2005). A method which finds the maxima and minima of a multivariable function applying affine arithmetic.

*LECTURE NOTES IN COMPUTER SCIENCE*,*3401*, 424-431.