
From:  Max Belushkin 
Subject:  Re: SV: [Helpgsl] On conjugate gradient algorithms in multidimentional minimisation problems. 
Date:  Mon, 05 Dec 2005 12:30:31 +0100 
Useragent:  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 FletcherReeves, PolakRibiere, vector BroydenFletcherGoldfarbShanno 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 #.FletcherReeves: small plateau at the start, large drop in chi squared, small plateau, bailed out. Chi squared reached: 6.54 by iteration 1200.
PolakRibiere: 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 outPlease share your findings once you had a chance to try different strategies. Another option would be try the optimizers in the TAO toolkit (http://wwwunix.mcs.anl.gov/tao/).  mj
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