scipy.optimize.BFGS¶

class scipy.optimize.BFGS(exception_strategy='skip_update', min_curvature=None, init_scale='auto')[source]¶

Broyden-Fletcher-Goldfarb-Shanno (BFGS) Hessian update strategy.

Parameters:

Parameters:	exception_strategy : {‘skip_update’, ‘damp_update’}, optional Define how to proceed when the curvature condition is violated. Set it to ‘skip_update’ to just skip the update. Or, alternatively, set it to ‘damp_update’ to interpolate between the actual BFGS result and the unmodified matrix. Both exceptions strategies are explained in [1], p.536-537. min_curvature : float This number, scaled by a normalization factor, defines the minimum curvature `dot(delta_grad, delta_x)` allowed to go unaffected by the exception strategy. By default is equal to 1e-8 when `exception_strategy = 'skip_update'` and equal to 0.2 when `exception_strategy = 'damp_update'`. init_scale : {float, ‘auto’} Matrix scale at first iteration. At the first iteration the Hessian matrix or its inverse will be initialized with `init_scale*np.eye(n)`, where `n` is the problem dimension. Set it to ‘auto’ in order to use an automatic heuristic for choosing the initial scale. The heuristic is described in [1], p.143. By default uses ‘auto’.

exception_strategy : {‘skip_update’, ‘damp_update’}, optional: Define how to proceed when the curvature condition is violated. Set it to ‘skip_update’ to just skip the update. Or, alternatively, set it to ‘damp_update’ to interpolate between the actual BFGS result and the unmodified matrix. Both exceptions strategies are explained in [1], p.536-537.
min_curvature : float: This number, scaled by a normalization factor, defines the minimum curvature dot(delta_grad, delta_x) allowed to go unaffected by the exception strategy. By default is equal to 1e-8 when exception_strategy = 'skip_update' and equal to 0.2 when exception_strategy = 'damp_update'.
init_scale : {float, ‘auto’}: Matrix scale at first iteration. At the first iteration the Hessian matrix or its inverse will be initialized with init_scale*np.eye(n), where n is the problem dimension. Set it to ‘auto’ in order to use an automatic heuristic for choosing the initial scale. The heuristic is described in [1], p.143. By default uses ‘auto’.

Notes

The update is based on the description in [1], p.140.

References

[1]	(1, 2, 3, 4) Nocedal, Jorge, and Stephen J. Wright. “Numerical optimization” Second Edition (2006).

Methods

`dot`(p)	Compute the product of the internal matrix with the given vector.
`get_matrix`()	Return the current internal matrix.
`initialize`(n, approx_type)	Initialize internal matrix.
`update`(delta_x, delta_grad)	Update internal matrix.