optimizer.py
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	#!/usr/bin/env python3
	# -- coding: utf-8 --
	"""
	Created on Thu Oct 10 10:19:11 2019
	Authors: Omid Ashtari and Armand Sieber
	Description: Scripts intended to minimize a quadratic function using scipy.optimize built-in function.
	The function to minimize is defined as S(X)= X'AX - X'B, with X = [x, y], X' the transform of X
	A is a 2x2 matrix and B 2X1 vector
	"""

	import numpy as np
	from scipy.optimize import minimize

	def objective(x, *args): #objective function to be minimized
	A = args[0]
	B = args[1].T
	S = np.dot(x.T, np.dot(A, x)) - np.dot(x.T, B)
	return S

	# Parameters of the unction to minimize
	A = np.array([[4, 0], [1, 3]])
	B = np.array([0, 1])

	# Initial guess
	X0 = np.array([3, 2])

	print(objective(X0, A, B))

	solution = minimize(objective, X0, args = (A, B), method = 'BFGS', options = {'xtol': 1e-12, 'maxiter':100})
	print(solution)