R: Shifted Limited-memory Variable-metric

varmetric {nloptr} | R Documentation

## Shifted Limited-memory Variable-metric

### Description

Shifted limited-memory variable-metric algorithm.

### Usage

    varmetric(x0, fn, gr = NULL, rank2 = TRUE, lower = NULL,
      upper = NULL, nl.info = FALSE, control = list(), ...)

### Arguments

`x0` | initial point for searching the optimum.
`fn` | objective function to be minimized.
`gr` | 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.

### Author(s)

Hans W. Borchers

### 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

[Package nloptr version 1.2.2.2 Index]