# scipy.optimize.BFGS

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

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

  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’.

  Notes

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

  References

  [1] (1,2,3)

  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.