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)

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 $(f^k-f^{k+1})/max\{|f^k|,|f^{k+1}|,1\}\le \text{ftol}$.

• 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