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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 simplified Jacobian matrix is stored in the integer
matrix of size (`M`, `m` `n`):
Gradient_Solve_General_Interval

called the *simplified jacobian*: the entry of this matrix
indicates for function and variable that
the gradient is always positive (1), the gradient is always
negative (-1), the function does not depend upon the variable (0), the
gradient may have not a constant sign within the range of the variable
(2).
The purpose of storing the simplified 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).
The algorithm try to manage the storage in order to solve the problem
with the given number `M`.
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 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.

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Jean-Pierre Merlet
2012-12-20