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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
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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 ??

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