What is the fastest way to minimize a function in python?

Question

So I have the following problem to minimize. I have a vector w that I need to find in order to minimize the following function:

import numpy as          


        

Answer 1

Based on pylang comments, I calculated the jacobian of my function which leads to the following function:

def fct_deriv(x):
    return 2 * matrix.dot(x)

The optimization problem becomes the following

minimize(fct, x0, method='SLSQP', jac=fct_deriv, bounds=bnds, constraints=cons)['x']

However, that solution does not allow to add the Hessian as the SLSQP method does not allow it. Other optimization methods exist, but SLSQP is the only one accepting bounds and constraints at the same time (which is central to my optimizatio problem).

See below for full code:

import numpy as np
from scipy.optimize import minimize

matrix = np.array([[1.0, 1.5, -2.],
                   [0.5, 3.0, 2.5],
                   [1.0, 0.25, 0.75]])

def fct(x):
    return x.dot(matrix).dot(x)

def fct_deriv(x):
    return 2 * matrix.dot(x)

x0 = np.ones(3) / 3
cons = ({'type': 'eq', 'fun': lambda x: x.sum() - 1.0})
bnds = [(0, 1)] * 3

w = minimize(fct, x0, method='SLSQP', jac=fct_deriv, bounds=bnds, constraints=cons)['x']

Edited (added the jacobian of the constraint):

cons2 = ({'type': 'eq', 'fun': lambda x: x.sum() - 1.0, 'jac': lambda x: np.ones_like(x)})

w = minimize(fct, x0, method='SLSQP', jac=fct_deriv, bounds=bnds, constraints=cons2)['x']