Non-linear programming; GNU licence/freeware alternatives for MATLAB fmincon?
My problem is related with the design of perfect reconstruction modulated filter banks. It is one component of the self-made lapped transform/filter bank toolbox for MATLAB. I've been utilizing optimization toolbox fmincon to solve minimization problems such as
min h^T Q h
c (h) = 0,
where h is a vector containing the coefficients of the real-valued
prototype filter, Q is a quadratic (or pos.def. ?) matrix and
the set of equality constraints c_n(h) are non-linear. More
precisely, the constraint equations can be given as
h^T C_n h - ScalarConstant = 0, but the nasty C_n is indefinite.
With "lowpass filter"-shaped initial value fmincon solves the problem above without difficulties. However, my interest is to make the LT/FB toolbox compatible with GNU OCTAVE, the free MATLAB-look-a-like. Currently the optimization routines that are included to the OCTAVE package can not solve the MFB design problem.
Now the actual question is:
Is there available GNU licence/freeware non-linear programming routines that is applicable with MFB design? I have exact functions for the gradients, also for the constraint equations. Yet one special feature in PR design is very strict constraint tolerance, in my MATLAB routine TolCon=.5e-14 is utilized.
Or has anybody bumped into a specialized code for this kind of purposes, since I know that there exists such.
Please, all suggestions are welcome as the optimization related issues are not my favorite playgroud.