Hi everyone,
I am interested in performing the free energy calculations for membrane proteins. I am following Justin Lemkul's tutorial for this. In the tutorial, it is mentioned that use of steepest descent with bfgs gives better results. How these algorithms are different to each other ?
I thought you may find this paper useful which compares SGD , L-BFGS and CG methods. "On Optimization Methods for Deep Learning" (Le, Ngiam et. al.)
Basically, BFGS is a Quasi-Newton algorithm and has a superlinear convergence, whereas the convergence of the steepest descent is linear. This can be a great difference in speed, especially in problems with ill-conditioned hessian matrix.
The drawback of BFGS is that it requires more memory - but as long as you fulfill the memory requirements, it will be more efficient.
If you are comparing methods of solving the Gibbs problem (free energy minimization) you should be aware that all classical approaches descend from the RAND algorithm, which is inherently unstable for all but ideal behavior of the constituents (i.e., Z=1). I have solved this problem, but have never published it. The solution works fine for liquids, solids, even near the critical point. It's already built into a computer program that you can download from my web site.
http://dudleybenton.altervista.org/software/CREST611.zip
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