scipy.optimize.fmin_cg

scipy.optimize.fmin_cg(f, x0, fprime=None, args=(), gtol=1.0000000000000001e-05, norm=inf, epsilon=1.4901161193847656e-08, maxiter=None, full_output=0, disp=1, retall=0, callback=None)

Minimize a function using a nonlinear conjugate gradient algorithm.

Parameters :

f : callable f(x,*args)

Objective function to be minimized.

x0 : ndarray

Initial guess.

fprime : callable f’(x,*args)

Function which computes the gradient of f.

args : tuple

Extra arguments passed to f and fprime.

gtol : float

Stop when norm of gradient is less than gtol.

norm : float

Order of vector norm to use. -Inf is min, Inf is max.

epsilon : float or ndarray

If fprime is approximated, use this value for the step size (can be scalar or vector).

callback : callable

An optional user-supplied function, called after each iteration. Called as callback(xk), where xk is the current parameter vector.

Returns :

xopt : ndarray

Parameters which minimize f, i.e. f(xopt) == fopt.

fopt : float

Minimum value found, f(xopt).

func_calls : int

The number of function_calls made.

grad_calls : int

The number of gradient calls made.

warnflag : int

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

allvecs : ndarray

If retall is True (see other parameters below), then this vector containing the result at each iteration is returned.

Other Parameters:  

maxiter : int

Maximum number of iterations to perform.

full_output : bool

If True then return fopt, func_calls, grad_calls, and warnflag in addition to xopt.

disp : bool

Print convergence message if True.

retall : bool

Return a list of results at each iteration if True.

Notes

Optimize the function, f, whose gradient is given by fprime using the nonlinear conjugate gradient algorithm of Polak and Ribiere. See Wright & Nocedal, ‘Numerical Optimization’, 1999, pg. 120-122.