leastsqbound on Rosenbrock function with a single bound

rosenbrock_leastsqbound.py

from __future__ import print_function

import numpy as np
from leastsqbound import leastsqbound


def fun(x):
    return np.array([10 * (x[1] - x[0]**2), (1 - x[0])])


def jac(x):
    return np.array([[-20 * x[0], 10],
                     [-1, 0]])


def main():
    x0 = np.array([2.0, 2.0])
    bounds = [(None, None), (1.5, None)]
    
    x_opt = np.array([1.22437075,  1.5])
    f_opt = fun(x_opt)
    obj_value_opt = np.dot(f_opt, f_opt)

    x, _ = leastsqbound(fun, x0, bounds=bounds, Dfun=jac)
    f = fun(x)
    obj_value = np.dot(f, f)

    x_num, _ = leastsqbound(fun, x0, bounds=bounds)
    f_num = fun(x_num)
    obj_value_num = np.dot(f_num, f_num)

    print(x_opt, obj_value_opt)
    print(x, obj_value)
    print(x_num, obj_value_num)
    
    # Output:
    # [ 1.22437075  1.5       ] 0.0504261878936
    # [ 1.          1.83336568] 69.4498361851
    # [ 1.22437075  1.50000001] 0.0504261888796


if __name__ == '__main__':
    main()