Non-linear programming; GNU licence/freeware alternatives for MATLAB fmincon?

Started by November 15, 2007
Greetings DSP enthusiastics and other earthlings,

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

subject to
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.
And sparse.

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.

J. Alhava