# scipy.optimize.fmin_ncg¶

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

Unconstrained minimization of a function using the Newton-CG method.

Parameters: 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), optional Function which computes the Hessian of f times an arbitrary vector, p. fhess : callable fhess(x, *args), optional Function to compute the Hessian matrix of f. args : tuple, optional 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, optional If fhess is approximated, use this value for the step size. callback : callable, optional An optional user-supplied function which is called after each iteration. Called as callback(xk), where xk is the current parameter vector. avextol : float, optional Convergence is assumed when the average relative error in the minimizer falls below this amount. maxiter : int, optional Maximum number of iterations to perform. full_output : bool, optional If True, return the optional outputs. disp : bool, optional If True, print convergence message. retall : bool, optional If True, return a list of results at each iteration. xopt : ndarray Parameters which minimize 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).

minimize
Interface to minimization algorithms for multivariate functions. See the ‘Newton-CG’ method in particular.

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.

Newton-CG methods are also called truncated Newton methods. This function differs from scipy.optimize.fmin_tnc because

1. scipy.optimize.fmin_ncg is written purely in python using numpy

and scipy while scipy.optimize.fmin_tnc calls a C function.

2. scipy.optimize.fmin_ncg is only for unconstrained minimization

while scipy.optimize.fmin_tnc is for unconstrained minimization or box constrained minimization. (Box constraints give lower and upper bounds for each variable separately.)

References

Wright & Nocedal, ‘Numerical Optimization’, 1999, pg. 140.

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