# lbfgs

##### Low-storage BFGS

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:

the optimal solution found so far.

the function value corresponding to `par`

.

number of (outer) iterations, see `maxeval`

.

integer code indicating successful completion (> 0) or a possible error number (< 0).

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.

##### 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

##### 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 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
# }
```

*Documentation reproduced from package nloptr, version 1.2.1, License: LGPL-3*