`scipy.optimize._optimize:fmin_bfgs`

source: /scipy/optimize/_optimize.py :1201

Signature

   def     fmin_bfgs (    f    ,    x0    ,    fprime    =  None   ,    args    =  ()   ,    gtol    =  1e-05   ,    norm    =  inf   ,    epsilon    =  1.4901161193847656e-08   ,    maxiter    =  None   ,    full_output    =  0   ,    disp    =  1   ,    retall    =  0   ,    callback    =  None   ,    xrtol    =  0   ,    c1    =  0.0001   ,    c2    =  0.9   ,    hess_inv0    =  None     )

Summary

Minimize a function using the BFGS algorithm.

Parameters

f : callable ``f(x,*args)``: Objective function to be minimized.
x0 : ndarray: Initial guess, shape (n,)
fprime : callable ``f'(x,*args)``, optional: Gradient of f.
args : tuple, optional: Extra arguments passed to f and fprime.
gtol : float, optional: Terminate successfully if gradient norm is less than gtol
norm : float, optional: Order of norm (Inf is max, -Inf is min)
epsilon : int or ndarray, optional: If fprime is approximated, use this value for the step size.
callback : callable, optional: An optional user-supplied function to call after each iteration. Called as callback(xk), where xk is the current parameter vector.
maxiter : int, optional: Maximum number of iterations to perform.
full_output : bool, optional: If True, return fopt, func_calls, grad_calls, and warnflag in addition to xopt.
disp : bool, optional: Print convergence message if True.
retall : bool, optional: Return a list of results at each iteration if True.
xrtol : float, default: 0: Relative tolerance for x. Terminate successfully if step size is less than xk * xrtol where xk is the current parameter vector.
c1 : float, default: 1e-4: Parameter for Armijo condition rule.
c2 : float, default: 0.9: Parameter for curvature condition rule.
hess_inv0 : None or ndarray, optional``: Initial inverse hessian estimate, shape (n, n). If None (default) then the identity matrix is used.

Returns

xopt : ndarray: Parameters which minimize f, i.e., f(xopt) == fopt.
fopt : float: Minimum value.
gopt : ndarray: Value of gradient at minimum, f'(xopt), which should be near 0.
Bopt : ndarray: Value of 1/f''(xopt), i.e., the inverse Hessian matrix.
func_calls : int: Number of function_calls made.
grad_calls : int: Number of gradient calls made.
warnflag : integer: 1Maximum number of iterations exceeded. 2 : Gradient and/or function calls not changing. 3 : NaN result encountered.
allvecs : list: The value of xopt at each iteration. Only returned if retall is True.

Notes

Optimize the function, f, whose gradient is given by fprime using the quasi-Newton method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS).

Parameters c1 and c2 must satisfy 0 < c1 < c2 < 1.

Examples

import numpy as np
from scipy.optimize import fmin_bfgs
def quadratic_cost(x, Q):
    return x @ Q @ x
x0 = np.array([-3, -4])
cost_weight =  np.diag([1., 10.])

✓

fmin_bfgs(quadratic_cost, x0, args=(cost_weight,))

✗

def quadratic_cost_grad(x, Q):
    return 2 * Q @ x

✓

fmin_bfgs(quadratic_cost, x0, quadratic_cost_grad, args=(cost_weight,))

✗

Aliases

scipy.optimize.fmin_bfgs