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# L_BFGS_B

class qiskit.algorithms.optimizers.L_BFGS_B(maxfun=15000, maxiter=15000, ftol=2.220446049250313e-15, iprint=-1, eps=1e-08, options=None, max_evals_grouped=1, **kwargs)

GitHub(opens in a new tab)

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(opens in a new tab)

Parameters

• maxfun (int(opens in a new tab)) – Maximum number of function evaluations.
• maxiter (int(opens in a new tab)) – 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(opens in a new tab)) – 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(opens in a new tab)) – If jac is approximated, use this value for the step size.
• options (dict(opens in a new tab) | None) – A dictionary of solver options.
• max_evals_grouped (int(opens in a new tab)) – Max number of default gradient evaluations performed simultaneously.
• kwargs – additional kwargs for scipy.optimize.minimize.

## Attributes

### bounds_support_level

Returns bounds 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_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

Return setting

## Methods

### get_support_level

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(opens in a new tab)) – the epsilon used in the numeric differentiation.
• max_evals_grouped (int(opens in a new tab)) – max evals grouped, defaults to 1 (i.e. no batching).

Returns

Return type

### minimize

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

Minimize the scalar function.

Parameters

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

set_max_evals_grouped(limit)

Set max evals grouped

### set_options

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(opens in a new tab)) – options, given as name=value.

### wrap_function

static wrap_function(function, args)

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

Parameters

Returns

wrapper

Return type

function_wrapper