I am curently using R package nleqslv for solving a non-linear system of equations with 300 variables. I need to scale this to the system with ~50k variables and naturally this does not scale very well, since the jacobian then takes up to ~30G of RAM, and I do not have access to a machine with such amount of RAM. The jacobian is a sparse matrix, but nleqslv does not have the ability to exploit this feature.
What are available solvers (preferably open source) which can exploit sparsity of the jacobian and can work with large systems?
I've searched around and found lots of software for optimization problems, which does not exactly suit me, since I am reluctant to minimize the sum of squares of the system. I can always hack nleqslv code to use sparse matrices, but first I would like to now what are available ready-made solutions.