On Mar 8, 2011, at 12:07 PM, [email protected] wrote:
I agree with that. In the NLopt implementation, however, SLSQP seems
to
perform a line search, while LBFGS does not (?). LBFGS evaluates the
gradient every time the function is called. This also affects
convergence. For a very small, randomly picked test with my
application,
I obtain the following results:
SLSQP: 54 gradients, 100 function evaluations, 28 seconds,
LBFGS: 116 gradients, 116 function evaluations, 67 seconds.
Perhaps, I am missing something here? According to the manual, the
gradient is required if and only if the gradient is not empty().
They both perform line searches (essentially any quasi-Newton method
must do this), but you are right in that SLSQP's line-search
implementation tries to avoid evaluating the gradient if it does not
need it. (The gradient is needed only for the first and last step of
the line search.)
It probably wouldn't be too hard to modify the LBFGS implementation to
do something similar.
Steven
PS. You can probably save a few more function evaluations if you check
for repeated calls with the same arguments. The reason is that, on
the line search, SLSQP often calls your function twice at the end of
the line search: once without the gradient, and then once more (when
it realizes ex post facto that the line search is done) with the
gradient. (An alternative interface would be to have separate
function calls for the objective and its gradient, but this is
problematic because the value and gradient usually share many
calculations.)
_______________________________________________
NLopt-discuss mailing list
[email protected]
http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/nlopt-discuss
