I want to perform constrained optimization of the function def F(X, data): # x1, x2, x3, t2 are scalars, data is a constant np.array x1, x2, x3, t2 = X T = np.arange(X.size) t1, t3 = T[0], T[-1] Xbefore = x1 + (T - t1) * (x2 - x1) / (t2 - t1) Xafter = x2 + (T - t2) * (x3 - x2) / (t3 - t2) Xbreak = np.where(T <= t2, Xbefore, Xafter) return ((Xbreak - data)**2).sum() where the parameter value t2 must be within 0 <= t2 < data.size. According to the tutorial (http://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html#constrained...), I need to define the Jacobian. However, I'm unsure of how to define the derivative with regards to t2. Any ideas are greatly appreciated :) Cheers, A.