Description: L-BFGS-B is a variant of the well-known "BFGS" quasi-Newton method. This variant uses limited-memory (like L-BFGS), and also handles simple constraints (to be specific, bound constraints, so this includes x >=0 constraints).
The authors of LBFGSB have had fortran implementations available since 1996, but in 2011 they released a major update (v3.0) which has an improved algorithm (you should use this version!). There are existing mex file wrappers for earlier versions, but none worked with v3.0, so I created this file.
This submission tries to make the mex wrapper simple, and then includes a nice .m file solver that requires very few parameters, yet is customizable for advanced users. Run the compile_mex.m file to compile the files. compile_mex.m also includes two quick sanity checks (the file driver1.m is a helper file for one of these checks)
I also have an example of using L-BFGS-B to solve the non-negative least-squares
(NNLS) problem, and comparing it to other existing solvers. To put it simply,
L-BFGS-B is a fantastic NNLS solver, and much better than Matlab's lsqnonneg.
The fortran lbfgsb is at http://users.eecs.northwestern.edu/~nocedal/lbfgsb.html,
There are also versions 2.1 and 2.4 of the library.
For v 2.1, Peter Carbonetto's mex interface works; see http://www.mathworks.com/matlabcentral/fileexchange/15061-matlab-interface-for-l-bfgs-b and also http://www.cs.ubc.ca/~pcarbo/lbfgsb-for-matlab.html
For v 2.4 (I don't know where you can find this version though), use the mex files from here: http://www.cs.toronto.edu/~liam/software.shtml
The wikipedia page (this was mainly edited by one of the authors of the L-BFGS-B algorithm): http://en.wikipedia.org/wiki/L-BFGS-B:_Optimization_subject_to_simple_bounds
For installing on 64-bit Windows, if you need a compiler, see http://www.mathworks.com/support/compilers/R2011b/win64.html
=== Update, Jan 2015 ===
I am not able to completely support installation/compiling of this toolbox. If you have issues, please mention in the comments below (there are also some solutions from other users in the comments below). Newer versions of Matlab keep changing how files compile (e.g., recent versions do not allow fortran and C to be compiled together), and I am not able to keep up.
If you are using mac or linux, there is a good chance that we can get it to compile. If you are using 64-bit Windows, there is a slim chance you can get it to compile. So please take this as a warning! If anyone is good at software installation and wants to take over the installation script, please do so. The actual wrapper script is quite simple.