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Re: SV: [Help-gsl] On conjugate gradient algorithms in multidimentional

From: Max Belushkin
Subject: Re: SV: [Help-gsl] On conjugate gradient algorithms in multidimentional minimisation problems.
Date: Mon, 05 Dec 2005 12:30:31 +0100
User-agent: Thunderbird 1.5 (X11/20051025)

    Hi everyone,

after extensive tests, here are the results. The tests were run on a simplified problem with an absolute minimum number of parameters (16) without any constraints.

For comparison, I ran the test on the Fletcher-Reeves, Polak-Ribiere, vector Broyden-Fletcher-Goldfarb-Shanno and a mm_hess algorithm [kindly provided by James in a private communication, I hope it makes it into his mlib].

The points at which the different algorithms bailed out are very close to each other in parameter space.

  Convergence was analyzed by recording the chi squared vs iteration #.

Fletcher-Reeves: small plateau at the start, large drop in chi squared, small plateau, bailed out. Chi squared reached: 6.54 by iteration 1200.

Polak-Ribiere: 4 plateaus on the way, reached chi squared 6.53 by iteration 5500.

  BFGS: 6 plateaus on the way, reached chi squared 6.53 by iteration 7800.

mm_hess: no plateaus, nice curve like 1/iteration #, reached chi squared 6.51 by iteration 23'300.

So far, it seems that the algorithms tend to the same point, none can actually converge. mm_hess takes more iterations, but finds a better chi squared, and if one measures stability by an absence of plateaus, this is a nice method, which, I hope, will be available in James' mlib some time...

I will run some tests on a problem with constraints, and see how the different algorithms fare there.

Martin Jansche wrote:
On 11/29/05, Max Belushkin <address@hidden> wrote:

James, thank you, I will certainly give it a go in the next couple of
days, and will let you know how it works out

Please share your findings once you had a chance to try different
strategies.  Another option would be try the optimizers in the TAO
toolkit (

-- mj

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