nloptr (version 2.0.3)

tnewton: Preconditioned Truncated Newton

Description

Truncated Newton methods, also calledNewton-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.

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.

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.

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

# NOT RUN {
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, 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

# }