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.
Details
Variable-metric methods are a variant of the quasi-Newton methods,
especially adapted to large-scale unconstrained (or bound constrained)
minimization.
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.
Note
Based on L. Luksan's Fortran implementation of a shifted limited-memory
variable-metric algorithm.
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