Adding an inequality to a linear program - recovering theorem via Delta of the Duals - Is this an old hat? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T20:25:05Z http://mathoverflow.net/feeds/question/78847 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/78847/adding-an-inequality-to-a-linear-program-recovering-theorem-via-delta-of-the-du Adding an inequality to a linear program - recovering theorem via Delta of the Duals - Is this an old hat? H. Georg Büsching 2011-10-22T20:15:28Z 2011-10-22T20:15:28Z <p>Is the theorem below already known?</p> <p>All inequalities can be transformed to the delta form. $$y_j: (y^0)_j^{-1} \sum_m \Delta^m(y^0_j) s_m \ge \omega(y^0_j) - \omega(y')$$</p> <p>As an inequality is only defined up to a factor, we can demand $(y^0)_j = 1$. \</p> <p>This is theorem 7.1 on page 21 of my <a href="http://www.optimization-online.org/DB_FILE/2011/03/2963.pdf" rel="nofollow">paper</a>.</p> <p>The proof is not really difficult, just see everything including the objective function as linear functions and use the two linear representation of the objective.</p> <p>This little theorem can be used to build a theory of creating new inequalities, when the inequalitiy system has additional properties like integrity for some variables. As it is so easily proved I would assume that it should be known. </p> <p>For sure the normal method from Mr. Balas is different.</p>