qiskit.aqua.components.optimizers.L_BFGS_B¶

class L_BFGS_B(maxfun=1000, maxiter=15000, factr=10, iprint=- 1, epsilon=1e-08)[source]¶

Limited-memory BFGS Bound optimizer.

The target goal of Limited-memory Broyden-Fletcher-Goldfarb-Shanno Bound (L-BFGS-B) is to minimize the value of a differentiable scalar function \(f\). This optimizer is a quasi-Newton method, meaning that, in contrast to Newtons’s method, it does not require \(f\)’s Hessian (the matrix of \(f\)’s second derivatives) when attempting to compute \(f\)’s minimum value.

Like BFGS, L-BFGS is an iterative method for solving unconstrained, non-linear optimization problems, but approximates BFGS using a limited amount of computer memory. L-BFGS starts with an initial estimate of the optimal value, and proceeds iteratively to refine that estimate with a sequence of better estimates.

The derivatives of \(f\) are used to identify the direction of steepest descent, and also to form an estimate of the Hessian matrix (second derivative) of \(f\). L-BFGS-B extends L-BFGS to handle simple, per-variable bound constraints.

Uses scipy.optimize.fmin_l_bfgs_b. For further detail, please refer to https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin_l_bfgs_b.html

Parameters

maxfun (int) – Maximum number of function evaluations.
maxiter (int) – Maximum number of iterations.
factr (float) – The iteration stops when (f^k - f^{k+1})/max{|f^k|, |f^{k+1}|,1} <= factr * eps, where eps is the machine precision, which is automatically generated by the code. Typical values for factr are: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy. See Notes for relationship to ftol, which is exposed (instead of factr) by the scipy.optimize.minimize interface to L-BFGS-B.
iprint (int) – Controls the frequency of output. iprint < 0 means no output; iprint = 0 print only one line at the last iteration; 0 < iprint < 99 print also f and |proj g| every iprint iterations; iprint = 99 print details of every iteration except n-vectors; iprint = 100 print also the changes of active set and final x; iprint > 100 print details of every iteration including x and g.
epsilon (float) – Step size used when approx_grad is True, for numerically calculating the gradient

__init__(maxfun=1000, maxiter=15000, factr=10, iprint=- 1, epsilon=1e-08)[source]¶

Parameters

maxfun (int) – Maximum number of function evaluations.
maxiter (int) – Maximum number of iterations.
factr (float) – The iteration stops when (f^k - f^{k+1})/max{|f^k|, |f^{k+1}|,1} <= factr * eps, where eps is the machine precision, which is automatically generated by the code. Typical values for factr are: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy. See Notes for relationship to ftol, which is exposed (instead of factr) by the scipy.optimize.minimize interface to L-BFGS-B.
iprint (int) – Controls the frequency of output. iprint < 0 means no output; iprint = 0 print only one line at the last iteration; 0 < iprint < 99 print also f and |proj g| every iprint iterations; iprint = 99 print details of every iteration except n-vectors; iprint = 100 print also the changes of active set and final x; iprint > 100 print details of every iteration including x and g.
epsilon (float) – Step size used when approx_grad is True, for numerically calculating the gradient

Methods

`__init__`([maxfun, maxiter, factr, iprint, …])	type maxfun `int`
`get_support_level`()	Return support level dictionary
`gradient_num_diff`(x_center, f, epsilon[, …])	We compute the gradient with the numeric differentiation in the parallel way, around the point x_center.
`optimize`(num_vars, objective_function[, …])	Perform optimization.
`print_options`()	Print algorithm-specific options.
`set_max_evals_grouped`(limit)	Set max evals grouped
`set_options`(**kwargs)	Sets or updates values in the options dictionary.
`wrap_function`(function, args)	Wrap the function to implicitly inject the args at the call of the function.

Attributes

`bounds_support_level`	Returns bounds support level
`gradient_support_level`	Returns gradient support level
`initial_point_support_level`	Returns initial point support level
`is_bounds_ignored`	Returns is bounds ignored
`is_bounds_required`	Returns is bounds required
`is_bounds_supported`	Returns is bounds supported
`is_gradient_ignored`	Returns is gradient ignored
`is_gradient_required`	Returns is gradient required
`is_gradient_supported`	Returns is gradient supported
`is_initial_point_ignored`	Returns is initial point ignored
`is_initial_point_required`	Returns is initial point required
`is_initial_point_supported`	Returns is initial point supported
`setting`	Return setting

property bounds_support_level¶: Returns bounds support level

get_support_level()[source]¶: Return support level dictionary

static gradient_num_diff(x_center, f, epsilon, max_evals_grouped=1)¶

We compute the gradient with the numeric differentiation in the parallel way, around the point x_center.

Parameters

x_center (ndarray) – point around which we compute the gradient
f (func) – the function of which the gradient is to be computed.
epsilon (float) – the epsilon used in the numeric differentiation.
max_evals_grouped (int) – max evals grouped

Returns

the gradient computed

Return type

grad

property gradient_support_level¶: Returns gradient support level

property initial_point_support_level¶: Returns initial point support level

property is_bounds_ignored¶: Returns is bounds ignored

property is_bounds_required¶: Returns is bounds required

property is_bounds_supported¶: Returns is bounds supported

property is_gradient_ignored¶: Returns is gradient ignored

property is_gradient_required¶: Returns is gradient required

property is_gradient_supported¶: Returns is gradient supported

property is_initial_point_ignored¶: Returns is initial point ignored

property is_initial_point_required¶: Returns is initial point required

property is_initial_point_supported¶: Returns is initial point supported

optimize(num_vars, objective_function, gradient_function=None, variable_bounds=None, initial_point=None)[source]¶

Perform optimization.

Parameters

num_vars (int) – Number of parameters to be optimized.
objective_function (callable) – A function that computes the objective function.
gradient_function (callable) – A function that computes the gradient of the objective function, or None if not available.
variable_bounds (list[(float, float)]) – List of variable bounds, given as pairs (lower, upper). None means unbounded.
initial_point (numpy.ndarray[float]) – Initial point.

Returns

point, value, nfev: point: is a 1D numpy.ndarray[float] containing the solution value: is a float with the objective function value nfev: number of objective function calls made if available or None

Raises

ValueError – invalid input

print_options()¶: Print algorithm-specific options.

set_max_evals_grouped(limit)¶: Set max evals grouped

set_options(**kwargs)¶

Sets or updates values in the options dictionary.

The options dictionary may be used internally by a given optimizer to pass additional optional values for the underlying optimizer/optimization function used. The options dictionary may be initially populated with a set of key/values when the given optimizer is constructed.

Parameters: kwargs (dict) – options, given as name=value.

property setting¶: Return setting

static wrap_function(function, args)¶

Wrap the function to implicitly inject the args at the call of the function.

Parameters

function (func) – the target function
args (tuple) – the args to be injected

Returns

wrapper

Return type

function_wrapper