# scipy.optimize.fmin_ncg¶

scipy.optimize.fmin_ncg(f, x0, fprime, fhess_p=None, fhess=None, args=(), avextol=1.0000000000000001e-05, epsilon=1.4901161193847656e-08, maxiter=None, full_output=0, disp=1, retall=0, callback=None)

Minimize a function using the Newton-CG method.

Parameters : Returns : f : callable f(x,*args) Objective function to be minimized. x0 : ndarray Initial guess. fprime : callable f’(x,*args) Gradient of f. fhess_p : callable fhess_p(x,p,*args) Function which computes the Hessian of f times an arbitrary vector, p. fhess : callable fhess(x,*args) Function to compute the Hessian matrix of f. args : tuple Extra arguments passed to f, fprime, fhess_p, and fhess (the same set of extra arguments is supplied to all of these functions). epsilon : float or ndarray If fhess is approximated, use this value for the step size. callback : callable An optional user-supplied function which is called after each iteration. Called as callback(xk), where xk is the current parameter vector. xopt : ndarray Parameters which minimizer f, i.e. f(xopt) == fopt. fopt : float Value of the function at xopt, i.e. fopt = f(xopt). fcalls : int Number of function calls made. gcalls : int Number of gradient calls made. hcalls : int Number of hessian calls made. warnflag : int Warnings generated by the algorithm. 1 : Maximum number of iterations exceeded. allvecs : list The result at each iteration, if retall is True (see below). avextol : float Convergence is assumed when the average relative error in the minimizer falls below this amount. maxiter : int Maximum number of iterations to perform. full_output : bool If True, return the optional outputs. disp : bool If True, print convergence message. retall : bool If True, return a list of results at each iteration.

Notes

Only one of fhess_p or fhess need to be given. If fhess is provided, then fhess_p will be ignored. If neither fhess nor fhess_p is provided, then the hessian product will be approximated using finite differences on fprime. fhess_p must compute the hessian times an arbitrary vector. If it is not given, finite-differences on fprime are used to compute it. See Wright & Nocedal, ‘Numerical Optimization’, 1999, pg. 140.

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