fmin_l_bfgs_b(func, x0, fprime = None, args = (), approx_grad = 0, bounds = None, m = 10, factr = 10000000.0, pgtol = 1.0000000000000001e-005, epsilon = 1e-008, iprint = -Const(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.
License of L-BFGS-B (Fortran code)
==================================
The version included here (in fortran code) is 2.1 (released in 1997). 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.
References
* R. H. Byrd, P. Lu and J. Nocedal. A Limited Memory Algorithm for Bound
Constrained Optimization, (1995), SIAM Journal on Scientific and
Statistical Computing , 16, 5, pp. 1190-1208.
* C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B,
FORTRAN routines for large scale bound constrained optimization (1997),
ACM Transactions on Mathematical Software, Vol 23, Num. 4, pp. 550 - 560.
API Documentation Generated by Endo, 2006-08-14