When you browse the source, you can see exactly what algorithm is being used--perhaps this can help answer some of your performance questions? For minimize_constrained, Sage calls the multivariate constrained optimization functions from scipy.optimize: either fmin_tnc (truncated Newton's method) or fmin_cobyla (Constrained Optimization BY Linear) or, if requested, fmin_l_bfgs_b (L-BFGS-B algorithm).