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# L_BFGS_B¶

class L_BFGS_B(maxfun=15000, maxiter=15000, ftol=2.220446049250313e-15, iprint=- 1, eps=1e-08, options=None, max_evals_grouped=1, **kwargs)[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/optimize.minimize-lbfgsb.html

Parameters
• maxfun (int) – Maximum number of function evaluations.

• maxiter (int) – Maximum number of iterations.

• ftol (float) – 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 (Optional[dict]) – A dictionary of solver options.

• max_evals_grouped (int) – Max number of default gradient evaluations performed simultaneously.

• kwargs – additional kwargs for scipy.optimize.minimize.

Methods

 get_support_level Return support level dictionary gradient_num_diff We compute the gradient with the numeric differentiation in the parallel way, around the point x_center. minimize Minimize the scalar function. print_options Print algorithm-specific options. set_max_evals_grouped Set max evals grouped set_options Sets or updates values in the options dictionary. wrap_function Wrap the function to implicitly inject the args at the call of the function.

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

setting

Return setting

settings
Return type

Dict[str, Any]