lbfgs function

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(),
  ...
)

Arguments

• x0: initial point for searching the optimum.
• fn: objective function to be minimized.
• gr: gradient of function fn; will be calculated numerically if not specified.
• lower, upper: lower and upper bound constraints.
• nl.info: logical; shall the original NLopt info been shown.
• control: list of control parameters, see nl.opts for help.
• ...: further arguments to be passed to the function.

Returns

List with components: - par: the optimal solution found so far.

• value: the function value corresponding to par.

• iter: number of (outer) iterations, see maxeval.

• convergence: integer code indicating successful completion (> 0) or a possible error number (< 0).

• message: character string produced by NLopt and giving additional information.

Details

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.

Note

Based on a Fortran implementation of the low-storage BFGS algorithm written by L. Luksan, and posted under the GNU LGPL license.

Examples

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  4

References

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).

See Also

optim

Author(s)

Hans W. Borchers