@inproceedings{miy-kas-05-aa-maxmin,
  author = {Miyajima, Shinya and Kashiwagi, Masahide},
  title = {A Method Which Finds the Maxima and Minima of a Multivariable Function Applying Affine Arithmetic},
  booktitle = {Proc. International Conference on Numerical Analysis and Its Applications (NAA 2004)},
  year = 2005,
  publisher = {Springer},
  pages = {424--431},
  isbn = {978-3-540-31852-1},
  comment = {Branch and bound, but with some improvements},
  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 subregions recursively and bounding the ranges of $f$ in the each subregion applying affine arithmetic and discarding the subregions which don't possess the possibility of including the point that the maximum (minimum) value occurs. Moreover, to discard more subregions 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.}
}