# tfg.math.optimizer.levenberg_marquardt.minimize

Minimizes a set of residuals in the least-squares sense.

`residuals` A residual or a list/tuple of residuals. A residual is a Python `callable`.
`variables` A variable or a list or tuple of variables defining the starting point of the minimization.
`max_iterations` The maximum number of iterations.
`regularizer` The regularizer is used to damped the stepsize when the iterations are becoming unstable. The bigger the regularizer is the smaller the stepsize becomes.
`regularizer_multiplier` If an iteration does not decrease the objective a new regularizer is computed by scaling it by this multiplier.
`callback` A callback function that will be called at each iteration. In graph mode the callback should return an op or list of ops that will execute the callback logic. The callback needs to be of the form f(iteration, objective_value, variables). A callback is a Python `callable`. The callback could be used for logging, for example if one wants to print the objective value at each iteration.
`name` A name for this op. Defaults to "levenberg_marquardt_minimize".

The value of the objective function and variables attained at the final iteration of the minimization procedure.

`ValueError` If max_iterations is not at least 1.
`InvalidArgumentError` This exception is only raised in graph mode if the Cholesky decomposition is not successful. One likely fix is to increase the regularizer. In eager mode this exception is catched and the regularizer is increased automatically.

#### Examples:

``````x = tf.constant(np.random.random_sample(size=(1,2)), dtype=tf.float32)
y = tf.constant(np.random.random_sample(size=(3,1)), dtype=tf.float32)

def f1(x, y):
return x + y

def f2(x, y):
return x * y

def callback(iteration, objective_value, variables):
def print_output(iteration, objective_value, *variables):
print("Iteration:", iteration, "Objective Value:", objective_value)
for variable in variables:
print(variable)
inp = [iteration, objective_value] + variables
return tf.py_function(print_output, inp, [])

minimize_op = minimize(residuals=(f1, f2),
variables=(x, y),
max_iterations=10,
callback=callback)

if not tf.executing_eagerly():
with tf.Session() as sess:
sess.run(tf.global_variables_initializer())
sess.run(minimize_op)
``````
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