R: Low-storage BFGS

lbfgs {nloptr} | R Documentation

## Low-storage BFGS

### Description

Low-storage version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.

### Usage

    lbfgs(x0, fn, gr = NULL, 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.
`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

The low-storage (or limited-memory) algorithm is a member of the class of quasi-Newton optimization methods. It is well suited for optimization problems with a large number of variables.

One parameter of this algorithm is the number `m` of gradients to remember from previous optimization steps. NLopt sets `m` to a heuristic value by default. It can be changed by the NLopt function `set_vector_storage`.

### 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 a Fortran implementation of the low-storage BFGS algorithm written by L. Luksan, and posted under the GNU LGPL license.

### Author(s)

Hans W. Borchers

### References

J. Nocedal, “Updating quasi-Newton matrices with limited storage,” Math. Comput. 35, 773-782 (1980).

D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Programming 45, p. 503-528 (1989).

### See Also

`optim`

### 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 <- lbfgs(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]