Certificates of linear mixed integer infeasibility

A central result in the theory of integer optimization states that a system of linear diophantine equations Ax = b has no integral solution if and only if there exists a vector in the dual lattice, yT A integral such that yT b is fractional. We extend this result to systems that both have equations and inequalities {Ax = b, Cx d}. We show that a certificate of integral infeasibility is a linear system with rank(C) variables containing no integral point. The result also extends to the mixed integer setting. Key words: Mixed integer programming, disjunction, split cuts

• Type: Journal
• Year: 2008
• Where: ORL
• Authors: Kent Andersen, Quentin Louveaux, Robert Weismantel
• Keywords: Integer, Integral, Linear Diophantine Equations, ORL 2008