L_BFGS_B

class L_BFGS_B(maxfun=1000, maxiter=15000, factr=10, iprint=- 1, epsilon=1e-08)

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/generated/scipy.optimize.fmin_l_bfgs_b.html

Parameters

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

• maxiter (int) – Maximum number of iterations.

• factr (float) – The iteration stops 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 (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 |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.

• epsilon (float) – Step size used when approx_grad is True, for numerically calculating the gradient

Attributes

L_BFGS_B.bounds_support_level	Returns bounds support level
L_BFGS_B.gradient_support_level	Returns gradient support level
L_BFGS_B.initial_point_support_level	Returns initial point support level
L_BFGS_B.is_bounds_ignored	Returns is bounds ignored
L_BFGS_B.is_bounds_required	Returns is bounds required
L_BFGS_B.is_bounds_supported	Returns is bounds supported
L_BFGS_B.is_gradient_ignored	Returns is gradient ignored
L_BFGS_B.is_gradient_required	Returns is gradient required
L_BFGS_B.is_gradient_supported	Returns is gradient supported
L_BFGS_B.is_initial_point_ignored	Returns is initial point ignored
L_BFGS_B.is_initial_point_required	Returns is initial point required
L_BFGS_B.is_initial_point_supported	Returns is initial point supported
L_BFGS_B.setting	Return setting

Methods

L_BFGS_B.get_support_level()	Return support level dictionary
L_BFGS_B.gradient_num_diff(x_center, f, epsilon)	We compute the gradient with the numeric differentiation in the parallel way, around the point x_center.
L_BFGS_B.optimize(num_vars, objective_function)	Perform optimization.
L_BFGS_B.print_options()	Print algorithm-specific options.
L_BFGS_B.set_max_evals_grouped(limit)	Set max evals grouped
L_BFGS_B.set_options(**kwargs)	Sets or updates values in the options dictionary.
L_BFGS_B.wrap_function(function, args)	Wrap the function to implicitly inject the args at the call of the function.