Scipy.optimize.minimize : Compute Hessian And Gradient Together

The scipy.optimize.minimize function implements basically the equivalent to MATLAB's 'fminunc' function for finding local minima of functions. In scipy, functions for the gradient

Solution 1:

You could go for a caching solution, but first numpy arrays are not hashable, and second you only need to cache a few values depending on whether the algorithm goes back and forth a lot on x. If the algorithm only moves from one point to the next, you can cache only the last computed point in this way, with your f_hes and f_jac being just lambda interfaces to a longer function computing both:

import numpy as np

# I choose the example f(x,y) = x**2 + y**2, with x,y the 1st and 2nd element of x below:deff(x):
    return x[0]**2+x[1]**2deff_jac_hess(x):
    ifall(x==f_jac_hess.lastx):
        print('fetch cached value')
        return f_jac_hess.lastf
    print('new elaboration')
    res = array([2*x[0],2*x[1]]),array([[2,0],[0,2]])

    f_jac_hess.lastx = x
    f_jac_hess.lastf = res

    return res

f_jac_hess.lastx = np.empty((2,)) * np.nan

f_jac = lambda x : f_jac_hess(x)[0]
f_hes = lambda x : f_jac_hess(x)[1]

Now the second call would cache the saved value:

>>> f_jac([3,2])
new elaboration
Out: [6, 4]
>>> f_hes([3,2])
fetch cached value
Out: [[2, 0], [0, 2]]

You then call it as:

minimize(f,array([1,2]),method='Newton-CG',jac = f_jac, hess= f_hes, options={'xtol': 1e-30, 'disp': True})