Shifted Limited-memory Variable-metric
Shifted limited-memory variable-metric algorithm.
varmetric(x0, fn, gr = NULL, rank2 = TRUE, 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 |
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 |
... |
further arguments to be passed to the function. |
Variable-metric methods are a variant of the quasi-Newton methods, especially adapted to large-scale unconstrained (or bound constrained) minimization.
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 L. Luksan's Fortran implementation of a shifted limited-memory variable-metric algorithm.
Hans W. Borchers
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).
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 4Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.