When the problem is very large, a limited-memory bfgs algorithm may be needed, if bfgsmin is not feasible due to memory limitations. lbfgsmin is called as
It is possible that lbfgsmin can outperform bfgsmin
even when memory is not an issue. Remember that both of these algorithms
are approximating the Hessian matrix using previous gradient
evaluations. If the true Hessian is changing rapidly, then a limited
memory approximation may be better than a long memory approximation.
The Rosenbrock function is such a case. The program lbfgsmin-example.m
minimizes a 200-dimensional Rosenbrock function using both algorithms.
The output
/home/sh/Dokumenter/octave/octave-forge/main/optim/doc/lbfgsmin-example.outshows that the limited memory algorithm uses significantly more iterations that the ordinary BFGS algorithm, but it is almost 4 times as fast. In general, though, the ordinary BFGS algorithm is recommended when memory limitations are not a problem.
Søren Hauberg 2008-04-29