:py:mod:`micom.duality`
=======================

.. py:module:: micom.duality

.. autoapi-nested-parse::

   Implements a fast dual formulation.



Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::

   micom.duality.fast_dual



.. py:function:: fast_dual(model, prefix='dual_')

   Add dual formulation to the problem.

   A mathematical optimization problem can be viewed as a primal and a dual
   problem. If the primal problem is a minimization problem the dual is a
   maximization problem, and the optimal value of the dual is a lower bound of
   the optimal value of the primal. For linear problems, strong duality holds,
   which means that the optimal values of the primal and dual are equal
   (duality gap = 0). This functions takes an optlang Model representing a
   primal linear problem
   and returns a new Model representing the dual optimization problem. The
   provided model must have a linear objective, linear constraints and only
   continuous variables. Furthermore, the problem must be in standard form,
   i.e. all variables should be non-negative. Both minimization and
   maximization problems are allowed.

   .. attribute:: model

      The model to be dualized.

      :type: cobra.Model

   .. attribute:: prefix

      The string that will be prepended to all variable and constraint names
      in the returned dual problem.

      :type: str

   :returns: The coefficients for the new dual objective.
   :rtype: dict