tnewton: Preconditioned Truncated Newton

In nloptr: R Interface to NLopt

Preconditioned Truncated Newton

Description

Truncated Newton methods, also called Newton-iterative methods, solve an approximating Newton system using a conjugate-gradient approach and are related to limited-memory BFGS.

Usage

tnewton(
  x0,
  fn,
  gr = NULL,
  lower = NULL,
  upper = NULL,
  precond = TRUE,
  restart = TRUE,
  nl.info = FALSE,
  control = list(),
  ...
)

Arguments

x0	starting point for searching the optimum.
fn	objective function that is to be minimized.
gr	gradient of function fn; will be calculated numerically if not specified.
lower, upper	lower and upper bound constraints.
precond	logical; preset L-BFGS with steepest descent.
restart	logical; restarting L-BFGS with steepest descent.
nl.info	logical; shall the original NLopt info been shown.
control	list of options, see nl.opts for help.
...	additional arguments passed to the function.

Details

Truncated Newton methods are based on approximating the objective with a quadratic function and applying an iterative scheme such as the linear conjugate-gradient algorithm.

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 (> 1) or a possible error number (< 0).
message	character string produced by NLopt and giving additional information.

Note

Less reliable than Newton's method, but can handle very large problems.

Author(s)

Hans W. Borchers

References

R. S. Dembo and T. Steihaug, “Truncated Newton algorithms for large-scale optimization,” Math. Programming 26, p. 190-212 (1982).

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 boundary
S <- tnewton(rep(3, 25L), flb, lower = rep(2, 25L), upper = rep(4, 25L),
       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

nloptr documentation built on July 4, 2024, 1:08 a.m.