fmin_l_bfgs_b(func, x0, fprime=None, args=(), approx_grad=0, bounds=None, m=10, factr=10000000.0, pgtol=1e-05, epsilon=1e-08, iprint=-1, maxfun=15000, maxiter=15000, disp=None, callback=None, maxls=20)

Notes

License of L-BFGS-B (FORTRAN code):

The version included here (in fortran code) is 3.0 (released April 25, 2011). It was written by Ciyou Zhu, Richard Byrd, and Jorge Nocedal <nocedal@ece.nwu.edu>. It carries the following condition for use:

This software is freely available, but we expect that all publications describing work using this software, or all commercial products using it, quote at least one of the references given below. This software is released under the BSD License.

Parameters

func : callable f(x,*args)

Function to minimize.

x0 : ndarray

Initial guess.

fprime : callable fprime(x,*args), optional

The gradient of :None:None:`func`. If None, then :None:None:`func` returns the function value and the gradient ( f, g = func(x, *args) ), unless :None:None:`approx_grad` is True in which case :None:None:`func` returns only f .

args : sequence, optional

Arguments to pass to :None:None:`func` and fprime .

approx_grad : bool, optional

Whether to approximate the gradient numerically (in which case :None:None:`func` returns only the function value).

bounds : list, optional

(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.

m : int, optional

The maximum number of variable metric corrections used to define the limited memory matrix. (The limited memory BFGS method does not store the full hessian but uses this many terms in an approximation to it.)

factr : float, optional

The iteration stops when (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr * eps , where eps is the machine precision, which is automatically generated by the code. Typical values for :None:None:`factr` are: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy. See Notes for relationship to :None:None:`ftol`, which is exposed (instead of :None:None:`factr`) by the scipy.optimize.minimize interface to L-BFGS-B.

pgtol : float, optional

The iteration will stop when max{|proj g_i | i = 1, ..., n} <= pgtol where pg_i is the i-th component of the projected gradient.

epsilon : float, optional

Step size used when :None:None:`approx_grad` is True, for numerically calculating the gradient

iprint : int, optional

Controls the frequency of output. iprint < 0 means no output; iprint = 0 print only one line at the last iteration; 0 < iprint < 99 print also f and |proj g| every iprint iterations; iprint = 99 print details of every iteration except n-vectors; iprint = 100 print also the changes of active set and final x; iprint > 100 print details of every iteration including x and g.

disp : int, optional

If zero, then no output. If a positive number, then this over-rides :None:None:`iprint` (i.e., :None:None:`iprint` gets the value of :None:None:`disp`).

maxfun : int, optional

Maximum number of function evaluations. Note that this function may violate the limit because of evaluating gradients by numerical differentiation.

maxiter : int, optional

Maximum number of iterations.

callback : callable, optional

Called after each iteration, as callback(xk) , where xk is the current parameter vector.

maxls : int, optional

Maximum number of line search steps (per iteration). Default is 20.

Returns

x : array_like

Estimated position of the minimum.

f : float

Value of :None:None:`func` at the minimum.

d : dict

Information dictionary.

• d['warnflag'] is

  • 0 if converged,

  • 1 if too many function evaluations or too many iterations,

  • 2 if stopped for another reason, given in d['task']

• d['grad'] is the gradient at the minimum (should be 0 ish)

• d['funcalls'] is the number of function calls made.

• d['nit'] is the number of iterations.

Minimize a function func using the L-BFGS-B algorithm.

See Also

minimize

Interface to minimization algorithms for multivariate functions. See the 'L-BFGS-B' :None:None:`method` in particular. Note that the :None:None:`ftol` option is made available via that interface, while :None:None:`factr` is provided via this interface, where :None:None:`factr` is the factor multiplying the default machine floating-point precision to arrive at :None:None:`ftol`: ftol = factr * numpy.finfo(float).eps .

Examples

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.optimize._lbfgsb_py._minimize_lbfgsb

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