(reoptimizer_problem_example_problem)=
# Sizing of a hollow bar example problem

In order to give a more detailed example of the usage of both local and global solvers, the hollow 
bar problem is introduced. It consists in finding the lengths of the internal and external sides of 
a hollow bar with a square section, minimising its weight (*i.e.* its section) and its deformation 
by an external force applied at its centre. The two lengths are normalised so that they evolved in a 
0 to 1 range and the pipe can be sketched as done in {numref}`reoptimizer_uranie_vizir_barre`.

{{
    "```{" "figure" "} " + parent_dir +
        "/usermanual/reoptimizer/figures/uranie_vizir_barre.png\n"
    ":align: center\n"
    ":name: reoptimizer_uranie_vizir_barre\n"
    + figure_scale + "\n"
    "\n"
    "Hollow Bar\n"
    "```"
}}

The problem has then three variables:

- $f_1(x,y) = x - y$ which is called the thickness.

- $f_2(x,y) = x^2 - y^2 $ which is called the section.

- $f_3(x,y) = (x^4 - y^4)^{-1}$ which is called the distortion

and three natural constraints:

- 0 < $x$ < 1.

- 0 < $y$ < 1.

- $x$ > $y$

In the following sections the idea will be to study (if possible) the minimisation of the section of 
the bar and the distortion, keeping a minimum thickness of about 0.4. This threshold is chosen so that 
the bar can sustain its own weight. The examples will use an external code to compute the three 
previously-introduced variables once both the internal and external lengths are provided. The code 
is written in python as following:

{{
    "```{literalinclude} " + parent_dir
    + "/roottest/uranie/references/reoptimizer/bar.py"
    + "\n"
    + ":language: python\n"
    + "```"
}}

In both examples, the same tip is used: the *bar.py* file is used to perform the computation (as the 
code is defined by `python bar.py > output.dat`) but it is also defined as the input file for the 
`TCode`. Thanks to this, the file is copied to every temporary working directory (so no need to change 
the `$PYTHONPATH` environment variable) and no extra file is needed to define the inputs. The output 
is directly stored as an ASCII file compatible with the usual {{salome}} table format so that it can 
easily be read and convert as a {{tds}}