scipy.optimize.fmin_tnc

scipy.optimize.fmin_tnc(func, x0, fprime=None, args=(), approx_grad=0, bounds=None, epsilon=1e-08, scale=None, offset=None, messages=15, maxCGit=-1, maxfun=None, eta=-1, stepmx=0, accuracy=0, fmin=0, ftol=-1, xtol=-1, pgtol=-1, rescale=-1)

Minimize a function with variables subject to bounds, using gradient information.

Parameters:

func : callable func(x, *args)

Function to minimize. Should return f and g, where f is the value of the function and g its gradient (a list of floats). If the function returns None, the minimization is aborted.

x0 : list of floats

Initial estimate of minimum.

fprime : callable fprime(x, *args)

Gradient of func. If None, then func must return the function value and the gradient (f,g = func(x, *args)).

args : tuple

Arguments to pass to function.

approx_grad : bool

If true, approximate the gradient numerically.

bounds : list

(min, max) pairs for each element in x, defining the bounds on that parameter. Use None or +/-inf for one of min or max when there is no bound in that direction.

scale : list of floats

Scaling factors to apply to each variable. If None, the factors are up-low for interval bounded variables and 1+|x] fo the others. Defaults to None

offset : float

Value to substract from each variable. If None, the offsets are (up+low)/2 for interval bounded variables and x for the others.

messages :

Bit mask used to select messages display during minimization values defined in the MSGS dict. Defaults to MGS_ALL.

maxCGit : int

Maximum number of hessian*vector evaluations per main iteration. If maxCGit == 0, the direction chosen is -gradient if maxCGit < 0, maxCGit is set to max(1,min(50,n/2)). Defaults to -1.

maxfun : int

Maximum number of function evaluation. if None, maxfun is set to max(100, 10*len(x0)). Defaults to None.

eta : float

Severity of the line search. if < 0 or > 1, set to 0.25. Defaults to -1.

stepmx : float

Maximum step for the line search. May be increased during call. If too small, it will be set to 10.0. Defaults to 0.

accuracy : float

Relative precision for finite difference calculations. If <= machine_precision, set to sqrt(machine_precision). Defaults to 0.

fmin : float

Minimum function value estimate. Defaults to 0.

ftol : float

Precision goal for the value of f in the stoping criterion. If ftol < 0.0, ftol is set to 0.0 defaults to -1.

xtol : float

Precision goal for the value of x in the stopping criterion (after applying x scaling factors). If xtol < 0.0, xtol is set to sqrt(machine_precision). Defaults to -1.

pgtol : float

Precision goal for the value of the projected gradient in the stopping criterion (after applying x scaling factors). If pgtol < 0.0, pgtol is set to 1e-2 * sqrt(accuracy). Setting it to 0.0 is not recommended. Defaults to -1.

rescale : float

Scaling factor (in log10) used to trigger f value rescaling. If 0, rescale at each iteration. If a large value, never rescale. If < 0, rescale is set to 1.3.

Returns:

x : list of floats

The solution.

nfeval : int

The number of function evaluations.

rc :

Return code as defined in the RCSTRINGS dict.

Seealso:

• scikits.openopt, which offers a unified syntax to call this and other solvers

• fmin, fmin_powell, fmin_cg, fmin_bfgs, fmin_ncg :

  multivariate local optimizers

• leastsq : nonlinear least squares minimizer

• fmin_l_bfgs_b, fmin_tnc, fmin_cobyla : constrained multivariate optimizers

• anneal, brute : global optimizers

• fminbound, brent, golden, bracket : local scalar minimizers

• fsolve : n-dimenstional root-finding

• brentq, brenth, ridder, bisect, newton : one-dimensional root-finding

• fixed_point : scalar fixed-point finder