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Binding to L-BFGS-B. These is a limited-memory quasi-Newton code for unconstrained and for bound-constrained optimization.

The authors of the original FORTRAN code expect that if you use their software in a publication, you quote one of these references:

- R. H. Byrd, P. Lu and J. Nocedal. A Limited Memory Algorithm for Bound Constrained Optimization, (1995), SIAM Journal on Scientific and Statistical Computing , 16, 5, pp. 1190-1208.
- C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization (1997), ACM Transactions on Mathematical Software, Vol 23, Num. 4, pp. 550-560.
- J.L. Morales and J. Nocedal. L-BFGS-B: Remark on Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization (2011), to appear in ACM Transactions on Mathematical Software.

Represent the memory space needed to solve a minimization problem. It is usually allocated automatically but it is possible to do it manually to, say, allocate it once only before a loop.

`Abnormal(f, msg)`

is raised if the routine terminated abnormally without being able to satisfy the termination conditions. In such an event, the variable `x`

(see `F.min`

) will contain the current best approximation found and `f`

is the value of the target function at `x`

. `msg`

is a message containing additional information (returned by the original FORTRAN code).

If the error message is not precise enough, it is recommended to turn printing on to understand what is the problem.

`type print = `

`| No`

(*No output is generated.

*)`| Last`

(*Print one line at the last iteration.

*)`| Every of int`

(*

*)`Every k`

prints the value of the function and |proj gradient| every`k`

iterations. Valid values are`0 <= k <= 98`

, otherwise the closer value in that interval is used.`| Details`

(*Print details of every iteration (except vectors).

*)`| All`

(*Print details of every iteration (except vectors) including changes of active set and final x.

*)`| Full`

(*Print details of every iteration including x and g.

*)

Control of the frequency at which information is outputted.

Holds informations on the current state of the computation that can help to decide whether to stop.

`module F : sig ... end`

Fortran Layout.

`module C : sig ... end`

C layout.

`val work : ?corrections:int -> int -> work`

`work n`

allocate the work space for a problem of size at most `n`

.

`val is_constrained : state -> bool`

Tells whether the problem is constrained.

`val nintervals : state -> int`

The total number of intervals explored in the search of Cauchy points.

`val nskipped_updates : state -> int`

The total number of skipped BFGS updates before the current iteration.

`val iter : state -> int`

The number of current iteration.

`val nupdates : state -> int`

The total number of BFGS updates prior the current iteration.

`val nintervals_current : state -> int`

The number of intervals explored in the search of Cauchy point in the current iteration.

`val neval : state -> int`

The total number of function and gradient evaluations.

`val neval_current : state -> int`

The number of function value or gradient evaluations in the current iteration.

`val previous_f : state -> float`

Returns f(x) in the previous iteration.

`val norm_dir : state -> float`

2-norm of the line search direction vector.

`val eps : state -> float`

The machine precision epsmch generated by the code.

`val time_cauchy : state -> float`

The accumulated time spent on searching for Cauchy points.

`val time_subspace_min : state -> float`

The accumulated time spent on subspace minimization.

`val time_line_search : state -> float`

The accumulated time spent on line search.

`val slope : state -> float`

The slope of the line search function at the current point of line search.

`val slope_init : state -> float`

The slope of the line search function at the starting point of the line search.

`val normi_grad : state -> float`

The infinity norm of the projected gradient

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