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1
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import numpy as np
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2
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3
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def fx01(x):
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4
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5
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return np.exp(-1.*np.linalg.norm(x)**2)
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6
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7
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def grad_fx01(x):
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8
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9
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return np.exp(-1.*np.linalg.norm(x)**2)*-2.*x
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10
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11
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def fx02(x):
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12
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13
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return np.power(x, 2) * np.exp(-x) - x
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14
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15
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def grad_fx02(x):
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16
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17
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return 2. * x * np.exp(-x) - np.power(x, 2) * np.exp(-x) - 1
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18
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19
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def ArmijoGD(fx, grad_fx, x0, alpha=0.2, beta=0.8, epsilon=2e-4, max_iter=3000):
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20
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21
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if alpha < 0 or alpha > 1 or beta < 0 or beta > 1:
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22
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print("Some of alpha or beta, out of range")
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23
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raise ValueError
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24
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25
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step = 1
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26
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x = x0
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27
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if x==0.5 or x==2:
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28
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print("x = {0}".format(x))
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29
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30
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while step < max_iter:
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31
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beta_k = 1
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32
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grad = grad_fx(x)
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33
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34
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while fx(x - beta_k*grad) > fx(x) - beta_k*alpha*(np.linalg.norm(grad)**2):
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35
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beta_k = beta_k * beta
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36
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x = x - beta_k*grad
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37
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38
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if np.linalg.norm(grad) < epsilon:
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39
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print("Almost Converged")
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40
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break
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41
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step += 1
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42
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print("{0} step -> x : {1}, f(x) : {2}".format(step, x, fx(x)))
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43
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44
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return x, fx(x)
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45
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46
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47
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48
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49
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ArmijoGD(fx01, grad_fx01, x)
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50
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ArmijoGD(fx02, grad_fx02, x0=0.5)
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51
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ArmijoGD(fx02, grad_fx02, x0=2)
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