For a hobby project I need to solve a series of quadratic programming problems each with

• about 1000 constraints, each of the form $x_i-x_j\le c_{ij}$
• the objective function is the sum of about 300 terms of the form $w_{ij}^2(x_i-x_j+d_{ij})^2$
• about a third of the variables are ignored by the objective function, and are just there to help organize the constraints.

I imagine there must be off-the-shelf solvers that can do this, but I'm quite new to this area, and the list of solvers at Wikipedia is not really helpful in terms of selecting which one to look into. Could someone help point me towards a good choice, please?

I'm looking for something that is free and with not too much of a learning curve just to put a problem into it and get a solution. Needing to write some glue code in C/C++, Java, Perl or the like is not a showstopper, however.

• Do you have any other requirements/restrictions? The gold standard QP solvers are CPLEX and Gurobi, which are commercial, but have free academic licenses. For open source solvers, IPOPT is a good general purpose nonlinear programming solver; I'd have to look around at open source QP solvers to refresh my memory. (Edit: CVXOPT is also a fine choice of open source solver, if you know Python.) – Geoff Oxberry Apr 22 '14 at 19:48
• @Geoff: Which kind of requirements/restrictions are you envisaging? Unfortunately, since I'm not in academia those commercial solvers are not an option. – hmakholm left over Monica Apr 22 '14 at 20:51