lbfgs | R Documentation |

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

```
lbfgs(
x0,
fn,
gr = NULL,
lower = NULL,
upper = NULL,
nl.info = FALSE,
control = list(),
...
)
```

`x0` |
initial point for searching the optimum. |

`fn` |
objective function to be minimized. |

`gr` |
gradient of function |

`lower` , `upper` |
lower and upper bound constraints. |

`nl.info` |
logical; shall the original NLopt info been shown. |

`control` |
list of control parameters, see |

`...` |
further arguments to be passed to the function. |

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`

.

List with components:

`par` |
the optimal solution found so far. |

`value` |
the function value corresponding to |

`iter` |
number of (outer) iterations, see |

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

`message` |
character string produced by NLopt and giving additional information. |

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

Hans W. Borchers

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).

`optim`

```
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
```

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