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## [Help-gsl] Multidimensional Minimisation

**From**: |
Alexandros Beskos |

**Subject**: |
[Help-gsl] Multidimensional Minimisation |

**Date**: |
Sun, 24 Oct 2004 18:34:41 +0100 |

**User-agent**: |
Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.2.1) Gecko/20030225 |

I try to use the multidimensional minimisation algorithms
and I am conserned about the parameters they use.
So the algorithms that use the gradient for the target function, say f,
use (among others) the command:

`int gsl_multimin_fdfminimizer_set (gsl_multimin_fdfminimizer * s,
``gsl_multimin_function_fdf *fdf, const gsl_vector * x, double step_size,
``double tol)
`

`What these algorithms do is to pick up a certain one-dimensional
``direction after considering the value, or the gradient of f at the
``current estimate of the minimum and then apply one of the available
``one-dimensional techniques. Now, the command I have written above is
``supposed to provide the parameters "tol" and "step size" for the
``directional one-dimensional minimisation. What I cannot understand is
``the meaning of the parameter "step_size". The one-dimensional methods
``are supposed to somehow bracket the minimum in an interval and in theory
``require as parameters the boundaries of such an interval. In a more
``advanced level there is also an algorithm that generates such an
``interval given two points. Is this what the "step_size" is doing ?
``Provide the second point for the initiation of the above interval
``identification algorithm ??
`

**[Help-gsl] Multidimensional Minimisation**,
*Alexandros Beskos* **<=**