lines 8-104 of file: example/abs_normal/simplex_method.hpp

{xrst_begin simplex_method}
{xrst_spell
   maxitr
   rl
   xout
}

abs_normal: Solve a Linear Program Using Simplex Method
#######################################################

Syntax
******

   *ok* = ``simplex_method`` ( *level* , *b* , *A* , *c* , *maxitr* , *xout* )

Prototype
*********
{xrst_literal
   // BEGIN PROTOTYPE
   // END PROTOTYPE
}

Source
******
This following is a link to the source code for this example:
:ref:`simplex_method.hpp-name` .

Problem
*******
We are given
:math:`A \in \B{R}^{m \times n}`,
:math:`b \in \B{R}^m`,
:math:`c \in \B{R}^n`.
This routine solves the problem

.. math::

   \begin{array}{rl}
   \R{minimize} &
   g^T x \; \R{w.r.t} \; x \in \B{R}_+^n
   \\
   \R{subject \; to} & A x + b \leq 0
   \end{array}

Vector
******
The type *Vector* is a
simple vector with elements of type ``double`` .

level
*****
This value is less than or equal two.
If *level*  == 0 ,
no tracing is printed.
If *level*  >= 1 ,
a trace :math:`x` and the corresponding objective :math:`z`
is printed at each iteration.
If *level*  == 2 ,
a trace of the simplex Tableau is printed at each iteration.

A
*
This is a :ref:`row-major<glossary@Row-major Representation>` representation
of the matrix :math:`A` in the problem.

b
*
This is the vector :math:`b` in the problem.

c
*
This is the vector :math:`c` in the problem.

maxitr
******
This is the maximum number of simplex iterations to try before giving up
on convergence.

xout
****
This argument has size is *n* and
the input value of its elements does no matter.
Upon return it is the primal variables corresponding to the problem solution.

ok
**
If the return value *ok* is true, a solution has been found.
{xrst_toc_hidden
   example/abs_normal/simplex_method.cpp
   example/abs_normal/simplex_method.xrst
}
Example
*******
The file :ref:`simplex_method.cpp-name` contains an example and test of
``simplex_method`` .

{xrst_end simplex_method}