scipy.optimize.fmin_l_bfgs_b

scipy.optimize.fmin_l_bfgs_b(func, x0, fprime=None, args=(), approx_grad=0, bounds=None, m=10, factr=10000000.0, pgtol=1.0000000000000001e-05, epsilon=1e-08, iprint=-1, maxfun=15000)

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

Arguments:

func – function to minimize. Called as func(x, *args)

x0 – initial guess to minimum

fprime – gradient of func. If None, then func returns the function

value and the gradient ( f, g = func(x, *args) ), unless approx_grad is True then func returns only f. Called as fprime(x, *args)

args – arguments to pass to function

approx_grad – if true, approximate the gradient numerically and func returns

only function value.

bounds – a list of (min, max) pairs for each element in x, defining

the bounds on that parameter. Use None for one of min or max when there is no bound in that direction

m – 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 – The iteration stops when

(f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr*epsmch

where epsmch is the machine precision, which is automatically generated by the code. Typical values for factr: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy.

pgtol – The iteration will stop when

max{|proj g_i | i = 1, ..., n} <= pgtol

where pg_i is the ith component of the projected gradient.

epsilon – step size used when approx_grad is true, for numerically

calculating the gradient

iprint – controls the frequency of output. <0 means no output.

maxfun – maximum number of function evaluations.

Returns: x, f, d = fmin_lbfgs_b(func, x0, ...)

x – position of the minimum f – value of func at the minimum d – dictionary of information from routine

d[‘warnflag’] is

0 if converged, 1 if too many function evaluations, 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.