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###

Storage

The boxes generated by the bisection process are stored in
an interval matrix:
Box_Solve_General_Interval(M,m)

while the corresponding Jacobian matrix is stored in the interval
matrix of size (`M`, `m` `n`):
Gradient_Solve_JH_Interval

The purpose of storing the gradient for each box
is to avoid to re-compute a gradient as soon as it has been
determined that a father of the box has already a gradient
with a constant sign. This has the drawback that for large problems
this storage will be also large: hence it is possible to avoid this
storage by setting the variable
`ALIAS_Store_Gradient`
to 0 (its default value is 1).
Note that here we store the *interval* gradient matrix and not the
*simplified* gradient matrix as in the solving procedure
involving only the Jacobian.
The algorithm try to manage the storage in order to solve the problem
with the given number `M` (see section 2.3.1.2).
As seen in
section 2.3.1.2 two storage modes are available, the
*Direct Storage* and the *Reverse Storage* modes, which
are
obtained by setting the global variable `Reverse_Storage` to 0
(the default value) or to the number of
unknowns+1.

For both modes
the algorithm will first run until the bisection of the
current box leads to a total number of boxes
which exceed the allowed total number.
It will then delete the boxes
in the list which have been already bisected, thereby freeing some
storage space
(usually larger for the reverse mode than for the direct
mode)
and will start again.

If the procedure has to be used more than once it is possible to speed
up the computation by allocating the storage space before calling the
procedure. Then you may indicate that the storage space has been
allocated beforehand by indicating a negative value for `M`, the
number of boxes being given by the absolute value of `M`.

** Next:** Improvement of the function
** Up:** Implementation
** Previous:** Hessian procedure
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Jean-Pierre Merlet
2012-12-20