lines 7-51 of file: example/abs_normal/abs_min_linear.cpp

{xrst_begin abs_min_linear.cpp}
{xrst_spell
   affine
   minimizer
}

abs_min_linear: Example and Test
################################

Purpose
*******
The function
:math:`f : \B{R}^3 \rightarrow \B{R}` defined by

.. math::
   :nowrap:

   \begin{eqnarray}
   f( x_0, x_1  )
   & = &
   | d_0 - x_0 | + | d_1 - x_0 | + | d_2 - x_0 |
   \\
   & + &
   | d_3 - x_1 | + | d_4 - x_1 | + | d_5 - x_1 |
   \\
   \end{eqnarray}

is affine, except for its absolute value terms.
For this case, the abs_normal approximation should be equal
to the function itself.
In addition, the function is convex and
:ref:`abs_min_linear-name` should find its global minimizer.
The minimizer of this function is
:math:`x_0 = \R{median}( d_0, d_1, d_2 )`
and
:math:`x_1 = \R{median}( d_3, d_4, d_5 )`

Source
******
{xrst_literal
   // BEGIN C++
   // END C++
}

{xrst_end abs_min_linear.cpp}