Optimality criterion for a class of nonlinear integer programs

Authors:
Kazuo Murota;Hiroo Saito;Robert Weismantel
Affiliations:
Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan and PRESTO, JST, Tokyo, Japan;Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan;Department of Mathematics/IMO, Otto-von-Guericke-University of Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany
Venue:
Operations Research Letters
Year:
2004

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Abstract

Graver's optimality conditions based on Hilbert bases apply to an integer program with linear equations and a linear objective function. We generalize this result to include a fairly large class of nonlinear objective functions. Our extension provides in particular a link between the superadditivity of the difference-objective function and the Hilbert bases of conic subpartitions of R^n.