nloptr (version 1.0.0)

lbfgs: Low-storage BFGS

Description

Low-storage version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.

Usage

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.

Value

  • List with components:
  • parthe optimal solution found so far.
  • valuethe function value corresponding to par.
  • iternumber of (outer) iterations, see maxeval.
  • convergenceinteger code indicating successful completion (> 0) or a possible error number (< 0).
  • messagecharacter 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.

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

Examples

Run this code
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

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