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.
Returns: 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).
See also
- 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
- scipy.optimize.fmin_ncg is written purely in python using numpy
and scipy while scipy.optimize.fmin_tnc calls a C function.
- 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.