Hello all. I am a relatively new user of python and scipy and I have been trying out scipy's optimization facilities. I am using scipy version 0.6.0, as distributed with Ubuntu 8.04. My exploration has centered around the minimization of x*x*y, subject to the equality constraint 2*x*x+y*y=3. In my experience, this problem is solved by introducing a Lagrange multiplier and minimizing the Lagrangian: L = x*x*y - lambda * ( 2*x*x+y*y-3 ) I have had no problem finding the desired solution via Newton-Raphson using the function and its first and second derivatives: import scipy.optimize as opt import numpy import numpy.linalg as l def f(r): x,y,lam=r return x*x*y -lam*(2*x*x+y*y-3) def g(r): x,y,lam=r return numpy.array([2*x*y-4*lam*x, x*x-2*lam*y, -(2*x*x+y*y-3)]) def h(r): x,y,lam=r return numpy.mat([[2.*y-4.*lam, 2.*x, -4.*x],[2.*x,-2.*lam,-2.*y],[-4.*x,-2.*y,0.]]) def NR(f, g, h, x0, tol=1e-5, maxit=100): "Find a local extremum of f (a root of g) using Newton-Raphson" x1 = numpy.asarray(x0) f1 = f(x1) for i in range(0,maxit): dx = l.solve(h(x1),g(x1)) ldx = numpy.sqrt(numpy.dot(dx,dx)) x2 = x1-dx f2 = f(x2) if(ldx < tol): # x is close enough df = numpy.abs(f1-f2) if(df < tol): # f is close enough return x2, f2, df, ldx, i x1=x2 f1=f2 return x2, f2, df, ldx, i print NR(f,g,h,[-2.,2.,3.],tol=1e-10) My Newton-Raphson iteration converges in 5 iterations, but I have had no success using any of the functions in scipy.optimize, for example: print opt.fmin_bfgs(f=f, x0=[-2.,2.,3.], fprime=g) print opt.fmin_ncg(f=f, x0=[-2.,2.,3.], fprime=g, fhess=h) neither of which converges. I am beginning to suspect some fundamental misunderstanding on my part. Could someone throw me a bone? Best regards Gísli