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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, np.array, ‘auto’}

      This parameter can be used to initialize the Hessian or its inverse. When a float is given, the relevant array is initialized to `np.eye(n) * init_scale`, where `n` is the problem dimension. Alternatively, if a precisely `(n, n)` shaped, symmetric array is given, this array will be used. Otherwise an error is generated. Set it to ‘auto’ in order to use an automatic heuristic for choosing the initial scale. The heuristic is described in [1], p.143. The default is ‘auto’.

  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.

  __matmul__ |

  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).