nloptr: tnewton – R documentation

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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.

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).

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, 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

nloptr

R Interface to NLopt

v1.2.2.2

LGPL-3

Authors

Jelmer Ypma [aut, cre], Steven G. Johnson [aut] (author of the NLopt C library), Hans W. Borchers [ctb], Dirk Eddelbuettel [ctb], Brian Ripley [ctb] (build process on multiple OS), Kurt Hornik [ctb] (build process on multiple OS), Julien Chiquet [ctb], Avraham Adler [ctb] (removal deprecated calls from tests, <https://orcid.org/0000-0002-3039-0703>)

Initial release

2020-07-02