diff --git a/hw1-conjugate-gradient/optimizer.py b/hw1-conjugate-gradient/optimizer.py
index a22b22b1..3282633b 100644
--- a/hw1-conjugate-gradient/optimizer.py
+++ b/hw1-conjugate-gradient/optimizer.py
@@ -1 +1,71 @@
 import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib import cm
+from mpl_toolkits.mplot3d import Axes3D
+import scipy.optimize
+
+# Global variables (in capital letters)
+
+# Initial guess to minimizer
+GUESS = np.array([4,4])
+
+# This array will contain the steps of the minimizer on its way to the minimum
+STEPS = GUESS.reshape(-1,2)
+
+# This function fills the STEPS array, and is used as input to scipy.optimize.minimize
+def my_callback(xk):
+    global STEPS
+    STEPS = np.vstack((STEPS, np.array(xk)))
+
+# This function returns the minimum value of the function func given as input
+# The second input is the initial guess of the minimum
+def find_minimum(func, guess):
+    result = scipy.optimize.minimize(func, x0 = guess, method='BFGS', callback=my_callback)
+    return result.x
+
+# This function implements S(x) as given in the exercise sheet
+def quadratic_function(x):
+
+    # create column vector of input array
+    x.reshape(-1, 1)
+
+    # create matrix and vector coefficients of S(x) given in exercise sheet
+    mat = np.array([[4, 0], [1, 3]])
+    vec = np.array([0, 1]).transpose()
+
+    # return S(x)
+    return (x.transpose() @ mat) @ x - x.transpose() @ vec
+
+
+# This function plots the S(x) surface and includes the path taken by the minimizer
+def plotting():
+    fig = plt.figure(figsize=(14,8))
+    axe = fig.add_subplot(111, projection="3d")
+    num_of_points = 100
+    xmax = ymax = -10
+    xmin = ymin = 10
+    X, Y = np.meshgrid(np.linspace(xmin,xmax,num_of_points), np.linspace(ymin,ymax,num_of_points))
+    Z = np.zeros_like(X)
+    for i in range(0,num_of_points):
+        for j in range(0, num_of_points):
+            Z[i,j] = quadratic_function( np.array([X[i,j], Y[i,j]]) )
+    sp = axe.plot_surface(X, Y, Z, cmap=cm.coolwarm)
+    axe.view_init(60, 100)
+    fig.colorbar(sp)
+
+    step_value = np.zeros(STEPS.shape[0])
+    for i in range(0, STEPS.shape[0]):
+        step_value[i] = quadratic_function( np.array([STEPS[i, 0], STEPS[i, 1]]) )
+    axe.plot(STEPS[:,0], STEPS[:,1], step_value, 'r*--')
+
+    axe.set_xlabel('x', fontsize=15)
+    axe.set_ylabel('y', fontsize=15)
+    axe.set_zlabel('       S(x,y)', fontsize=15)
+    axe.zaxis.set_rotate_label(False)
+    plt.savefig("plot.png")
+    plt.show()
+
+result = find_minimum(quadratic_function, GUESS)
+print("The (approximated) minimum value is found at position (x,y) = ", result)
+print("The (approximated) minimum value is ", quadratic_function(result))
+plotting()