lines 7-40 of file: example/abs_normal/abs_min_quad.cpp

{xrst_begin abs_min_quad.cpp}
{xrst_spell
   minimizer
}

abs_min_quad: Example and Test
##############################

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

.. math::

   f( x_0, x_1  )
   =
   ( x_0^2 + x_1^2 ) / 2 +  | x_0 - 5 | + | x_1 + 5 |

For this case, the :ref:`abs_min_quad-name` object should be equal
to the function itself.
In addition, the function is convex and
:ref:`abs_min_quad-name` should find its global minimizer.
The minimizer of this function is
:math:`x_0 = 1`, :math:`x_1 = -1`.

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

{xrst_end abs_min_quad.cpp}