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Do you know some good free Matlab LBFGS implementations?
The only one I know (and use for the moment) is Liam Stewart's (it can be found at the following link: http://www.cs.toronto.edu/~liam/software.shtml)
My interest is using these algorithms in shape optimization problems, where the sizes of the problems tend to get very large.
Do you have any other suggestions of good and fast packages that can be used for optimizatioin problems?
The 'minFunc' MATLAB package (by Mark Schmidt) is one of the best available: http://www.di.ens.fr/~mschmidt/Software/minFunc.html
This package is fairly mature and has been widely used in the ML community. It contains a stable L-BFGS implementation as well as related Newton and quasi-Newton optimization methods.
A good Matlab implementation of limited-memory BFGS is the one accompanying Tim Kelley's book Iterative Methods for Optimization (SIAM, 1999; PDF freely downloadable from the publisher's website). You can find his Matlab codes here.
Regarding your second question: I would suggest implementing the algorithm yourself, since it is then much easier to adapt to the special structure of your specific problem (parameter tuning, exploiting derivative information, etc.).
