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Re: [Help-gsl] Rationale behind intermediate_point()

From: Johan Hattne
Subject: Re: [Help-gsl] Rationale behind intermediate_point()
Date: Tue, 19 Oct 2010 09:09:46 -0500

On 12 Oct 2010, at 08:10, Brian Gough wrote:

> At Fri, 08 Oct 2010 12:07:18 -0500,
> Johan Hattne wrote:
>> While comparing two different implementations of a multidimensional
>> optimiser I noticed the backtracking algorithm implemented in
>> intermediate_point() in GSL's multimin/directional_minimize.c.  It's not
>> obvious to me why the step size is decreased the way it is, i.e.
>>  step <- 0.5 * step * u / (df + u)
>> where u is the length of the step along the line on which a minimum is
>> sought, and df = f(x0 + u) - f(x0).  Could anyone enlighten me as to
>> what's the rationale behind this?
> It looks like the minimum of a quadratic given f(x0), f'(x0) and f(x0+u).

Ah... now I see (I think)!  As far as I can tell then, intermediate_point() is 
equivalent to the lnsrch() function (under the "Line Searching and 
Backtracking" heading of section 9.7 the Numerical Recipes) with the exception 
that it doesn't switch to a cubic approximation on subsequent backtracks, and 
that the stopping criterion is not "Armijo-like".  Correct?

// Best wishes; Johan

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