Low-storage BFGS
Low-storage version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.
lbfgs(x0, fn, gr = NULL, lower = NULL, upper = NULL, nl.info = FALSE, control = list(), ...)
x0 |
initial point for searching the optimum. |
fn |
objective function to be minimized. |
gr |
gradient of function |
lower, upper |
lower and upper bound constraints. |
nl.info |
logical; shall the original NLopt info been shown. |
control |
list of control parameters, see |
... |
further arguments to be passed to the function. |
The low-storage (or limited-memory) algorithm is a member of the class of quasi-Newton optimization methods. It is well suited for optimization problems with a large number of variables.
One parameter of this algorithm is the number m of gradients to
remember from previous optimization steps. NLopt sets m to a
heuristic value by default. It can be changed by the NLopt function
set_vector_storage.
List with components:
par |
the optimal solution found so far. |
value |
the function value corresponding to |
iter |
number of (outer) iterations, see |
convergence |
integer code indicating successful completion (> 0) or a possible error number (< 0). |
message |
character string produced by NLopt and giving additional information. |
Based on a Fortran implementation of the low-storage BFGS algorithm written by L. Luksan, and posted under the GNU LGPL license.
Hans W. Borchers
J. Nocedal, “Updating quasi-Newton matrices with limited storage,” Math. Comput. 35, 773-782 (1980).
D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Programming 45, p. 503-528 (1989).
flb <- function(x) {
p <- length(x)
sum(c(1, rep(4, p-1)) * (x - c(1, x[-p])^2)^2)
}
# 25-dimensional box constrained: par[24] is *not* at the boundary
S <- lbfgs(rep(3, 25), flb, lower=rep(2, 25), upper=rep(4, 25),
nl.info = TRUE, control = list(xtol_rel=1e-8))
## Optimal value of objective function: 368.105912874334
## Optimal value of controls: 2 ... 2 2.109093 4Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.