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# 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)

  Minimize a function using the BFGS algorithm.

  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 succesful 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 Results at each iteration. Only returned if retall is True.

  See also

  `minimize`
    Interface to minimization algorithms for multivariate functions. See the ‘BFGS’ method in particular.

  Notes

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

  References

  Wright, and Nocedal ‘Numerical Optimization’, 1999, pg. 198.

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