L_BFGS_B¶

class L_BFGS_B(maxfun=15000, maxiter=15000, ftol=np.float64(2.220446049250313e-15), iprint=-1, eps=1e-08, options=None, max_evals_grouped=1, **kwargs)[source]¶

Bases: SciPyOptimizer

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/optimize.minimize-lbfgsb.html

Parameters:

maxfun (int) – Maximum number of function evaluations.
maxiter (int) – Maximum number of iterations.
ftol (SupportsFloat) – The iteration stops when \((f^k - f^{k+1}) / \max\{|f^k|, |f^{k+1}|,1\} \leq \text{ftol}\).
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 \(|\text{proj} g|\) 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 \(g\).
eps (float) – If jac is approximated, use this value for the step size.
options (dict | None) – A dictionary of solver options.
max_evals_grouped (int) – Max number of default gradient evaluations performed simultaneously.
kwargs – additional kwargs for scipy.optimize.minimize.

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

settings¶

Methods

get_support_level()¶: Return support level dictionary

static gradient_num_diff(x_center, f, epsilon, max_evals_grouped=None)¶

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, defaults to 1 (i.e. no batching).

Returns:

the gradient computed

Return type:

grad

minimize(fun, x0, jac=None, bounds=None)¶

Minimize the scalar function.

Parameters:

fun (Callable[[float | ndarray], float]) – The scalar function to minimize.
x0 (float | ndarray) – The initial point for the minimization.
jac (Callable[[float | ndarray], float | ndarray] | None) – The gradient of the scalar function fun.
bounds (list[tuple[float, float]] | None) – Bounds for the variables of fun. This argument might be ignored if the optimizer does not support bounds.

Returns:

The result of the optimization, containing e.g. the result as attribute x.

Return type:

OptimizerResult

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.

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