scipy.optimize.fmin_bfgs¶

scipy.optimize.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)[source]¶

Minimize a function using the BFGS algorithm.

Parameters:

Parameters:	f : callable f(x,args) Objective function to be minimized. x0 : ndarray Initial guess. fprime* : callable f’(x,args), optional Gradient of f. args* : tuple, optional Extra arguments passed to f and fprime. gtol : float, optional Gradient norm must be less than gtol before successful termination. 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.
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 1 : Maximum number of iterations exceeded. 2 : Gradient and/or function calls not changing. allvecs : list `OptimizeResult` at each iteration. Only returned if retall is True.

f : callable f(x,*args)

Objective function to be minimized.

x0 : ndarray

Initial guess.

fprime : callable f’(x,*args), optional

Gradient of f.

args : tuple, optional

Extra arguments passed to f and fprime.

gtol : float, optional

Gradient norm must be less than gtol before successful termination.

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.

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

1 : Maximum number of iterations exceeded. 2 : Gradient and/or function calls not changing.

allvecs : list

OptimizeResult at each iteration. Only returned if retall is True.