Ex15_4.py

import numpy as np
from numpy.linalg import norm
from ipsolver import equality_constrained_sqp


def fun(x):
    return 2*(x[0]**2 + x[1]**2 - 1) - x[0]

def grad(x):
    return np.array([4*x[0]-1, 4*x[1]])

def hess(x, v):
    hess_fun = 4*np.eye(2)
    hess_constr = 2*np.eye(2)
    return hess_fun + v*hess_constr

def constr(x):
    return np.array([x[0]**2 + x[1]**2 - 1])

def jac(x):
    return np.array([[4*x[0]-1, 4*x[1]]])

x0 = np.array([0.7, 0.7])

x, info = equality_constrained_sqp(fun, grad, hess,
                                   constr, jac, x0,
                                   initial_trust_radius=1,
                                   initial_penalty=10,
                                   return_all=True)

print('f = '+ str(info["fun"]))
print('optimality = ' + str(info["opt"]))
print('c violation = ' + str(info["constr_violation"]))
print('niter = ' + str(info["niter"]))