# Source code for qiskit.algorithms.optimizers.l_bfgs_b

```
# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 2020.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""Limited-memory BFGS Bound optimizer."""
import warnings
from typing import Optional
import numpy as np
from qiskit.utils.deprecation import deprecate_arguments
from .scipy_optimizer import SciPyOptimizer
[docs]class L_BFGS_B(SciPyOptimizer): # pylint: disable=invalid-name
"""
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 :math:`f`.
This optimizer is a quasi-Newton method, meaning that, in contrast to Newtons's method,
it does not require :math:`f`'s Hessian (the matrix of :math:`f`'s second derivatives)
when attempting to compute :math:`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 :math:`f` are used to identify the direction of steepest descent,
and also to form an estimate of the Hessian matrix (second derivative) of :math:`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
"""
_OPTIONS = ["maxfun", "maxiter", "ftol", "iprint", "eps"]
# pylint: disable=unused-argument
@deprecate_arguments({"epsilon": "eps"})
def __init__(
self,
maxfun: int = 1000,
maxiter: int = 15000,
ftol: float = 10 * np.finfo(float).eps,
factr: Optional[float] = None,
iprint: int = -1,
epsilon: float = 1e-08,
eps: float = 1e-08,
options: Optional[dict] = None,
max_evals_grouped: int = 1,
**kwargs,
):
r"""
Args:
maxfun: Maximum number of function evaluations.
maxiter: Maximum number of iterations.
ftol: The iteration stops when (f\^k - f\^{k+1})/max{\|f\^k\|,\|f\^{k+1}\|,1} <= ftol.
factr: (DEPRECATED) The iteration steps 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: 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.
eps: If jac is approximated, use this value for the step size.
epsilon: (DEPRECATED) Step size used when approx_grad is True, for numerically
calculating the gradient
options: A dictionary of solver options.
max_evals_grouped: Max number of default gradient evaluations performed simultaneously.
kwargs: additional kwargs for scipy.optimize.minimize.
"""
if factr is not None:
warnings.warn(
"L_BFGS_B.__init__() keyword argument factr is deprecated and replaced with ftol. "
"The relationship between the two is ftol = factr * numpy.finfo(float).eps. "
"See https://docs.scipy.org/doc/scipy/reference/optimize.minimize-lbfgsb.html.",
DeprecationWarning,
stacklevel=2,
)
ftol = factr * np.finfo(float).eps
if options is None:
options = {}
for k, v in list(locals().items()):
if k in self._OPTIONS:
options[k] = v
super().__init__(
method="L-BFGS-B",
options=options,
max_evals_grouped=max_evals_grouped,
**kwargs,
)
```