clickoptim.py

# maximize abc subject to a + b + c = 10

import numpy as np
import tensorflow as tf

tf.reset_default_graph() 
abc = tf.get_variable("abc",shape=(3,1),dtype=tf.float32, initializer=tf.ones_initializer)
optimizer = tf.train.GradientDescentOptimizer(0.0001)

# grab a, b, c and the lambda l
a = abc[0,0]
b = abc[1,0]
c = abc[2,0]
l = tf.Variable(1.0, tf.float32)

f = a * b * c
g = a + b + c - 10.0

# standard lagrangian: gradient f = lambda * gradient g
flg = f - l * g  

# minimize lagrangian w.r.t each variate
traina = optimizer.minimize(tf.reduce_mean(tf.gradients( flg,a )))
trainb = optimizer.minimize(tf.reduce_mean(tf.gradients( flg,b )))
trainc = optimizer.minimize(tf.reduce_mean(tf.gradients( flg,c )))
trainl = optimizer.minimize(tf.reduce_mean(tf.gradients( flg,l )))

# maximize abc => minimize -abc
trainprod = optimizer.minimize(-f)

# minimize g^2
trainsum = optimizer.minimize(tf.square(g))

with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    n_iterations = 10000
    for iteration in range(n_iterations):
        sess.run([traina,trainb,trainc,trainl,trainprod, trainsum])
        print(a.eval())
        print(b.eval())
        print(c.eval())