I'm in search for a library for solving large systems of non-linear equations, similar to MINPACK, but unlike MINPACK, can accept a Jacobian in band-storage.
My Jacobian is sometimes not invertible, so a method like the Levenberg-Marquardt algorithm in MINPACK, which can deal with singular Jacobians is important. Also, it would be nice if the package was in Fortran, but C/C++ is ok too.
I'm solving a system of ~10,000 nonlinear equations, with a non-zero diagonal about ~200 wide, so using band-storage is necessary. Thanks for any suggestions.