If it turns out you don’t need arbitrary precision after all then you might want to try Gurobi. The latest version can handle large nonconvex quadratic problems. It may be helpful even if your problem is too large to solve to the global optimum before the end of the universe because it provides bounds on the global optimum. This can help you evaluate local optima from IPOPT or Gurobi’s own solve sequence.
Here’s a presentation that explains how the algorithm works:
