函数优化实战 - 好文

目录

* Himmelblau function
<https://www.cnblogs.com/nickchen121/p/10915301.html#himmelblau-function>
* Minima <https://www.cnblogs.com/nickchen121/p/10915301.html#minima>
* Plot <https://www.cnblogs.com/nickchen121/p/10915301.html#plot>
* Gradient Descent
<https://www.cnblogs.com/nickchen121/p/10915301.html#gradient-descent>
Himmelblau function

* \(f(x,y)=(x^2+y-11)^2+(x+y^2-7)^2\)

Minima

* f(3.0,2.0)=0.0
* f(-2.8,3.1)=0.0
* f(-3.7,-3.2)=0.0
* f(3.5,-1.84)=0.0
Plot
import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d
import Axes3D def himmeblau(x): return (x[0]**2 + x[1] - 11)**2 + (x[0] +
x[1]**2 - 7)**2 x = np.arange(-6, 6, 0.1) y = np.arange(-6, 6, 0.1)
print(f'x_shape: {x.shape},y_shape: {y.shape}') # 生成坐标点 X, Y = np.meshgrid(x,
y) print(f'X_shape: {X.shape},Y_shape: {Y.shape}') Z = himmeblau([X, Y]) fig =
plt.figure('himmelblau') ax = Axes3D(fig) ax.plot_surface(X, Y, Z)
ax.view_init(60, -30) ax.set_xlabel('x') ax.set_ylabel('y') plt.show() x_shape:
(120,),y_shape: (120,) X_shape: (120, 120),Y_shape: (120, 120)

Gradient Descent
import tensorflow as tf x = tf.constant([-4.,0.]) for step in range(200): with
tf.GradientTape() as tape: tape.watch([x]) y = himmeblau(x) grads =
tape.gradient(y,[x])[0] x -= 0.01 * grads if step % 20 == 0: print(f'step:
{step}, x: {x}, f(x): {y}') step: 0, x: [-2.98 -0.09999999], f(x): 146.0 step:
20, x: [-3.6890159 -3.1276689], f(x): 6.054703235626221 step: 40, x:
[-3.7793102 -3.283186 ], f(x): 0.0 step: 60, x: [-3.7793102 -3.283186 ], f(x):
0.0 step: 80, x: [-3.7793102 -3.283186 ], f(x): 0.0 step: 100, x: [-3.7793102
-3.283186 ], f(x): 0.0 step: 120, x: [-3.7793102 -3.283186 ], f(x): 0.0 step:
140, x: [-3.7793102 -3.283186 ], f(x): 0.0 step: 160, x: [-3.7793102 -3.283186
], f(x): 0.0 step: 180, x: [-3.7793102 -3.283186 ], f(x): 0.0

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