nloptr (version 2.2.0)

varmetric: Shifted Limited-memory Variable-metric

Description

Shifted limited-memory variable-metric algorithm.

Usage

varmetric(
  x0,
  fn,
  gr = NULL,
  rank2 = TRUE,
  lower = NULL,
  upper = NULL,
  nl.info = FALSE,
  control = list(),
  ...
)

Value

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.

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.

rank2

logical; if true uses a rank-2 update method, else rank-1.

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.

Author

Hans W. Borchers

Details

Variable-metric methods are a variant of the quasi-Newton methods, especially adapted to large-scale unconstrained (or bound constrained) minimization.

References

J. Vlcek and L. Luksan, ``Shifted limited-memory variable metric methods for large-scale unconstrained minimization,'' J. Computational Appl. Math. 186, p. 365-390 (2006).

See Also

lbfgs

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 <- varmetric(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