- Generating functions and duality for integer programs Jean B. Lasserre (lasserrelaas.fr) Abstract: We consider the integer program P -> max {c'x | Ax=y; x\in N^n }. Using the generating function of an associated counting problem, and a generalized residue formula of Brion and Vergne, we explicitly relate P with its continuous linear programming (LP) analogue and provide a characterization of its optimal value. In particular, dual variables $\lambda\in R^m$ have discrete analogues $z\in C^m$, related in a simple manner. Moreover, both optimal values of P and the LP obey the same formula, using z for P and |z| for the LP. One retrieves (and refines) the so-called group-relaxations of Gomory which, in this dual approach, arise naturally from a detailed analysis of a generalized residue formula of Brion and Vergne. Finally, we also provide an explicit formulation of a dual problem P*, an analogue of the dual LP in linear programming. Keywords: generating functions; integer programming; duality Category 1: Integer Programming Category 2: Global Optimization (Theory ) Citation: Discrete Optimization 1 (2004), pp. 167--187. Download: Entry Submitted: 12/02/2003Entry Accepted: 12/02/2003Entry Last Modified: 09/23/2005Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.