Optimality Criteria for a Class of Multi-Objective Nonlinear Integer Programs

This paper studies the Graver's optimality conditions for multi-objective non-linear integer programming problem based on Hilbert basis. Here, the result is generalized to include a fairly large class of multi-objective non-linear objective functions.  This extension provides in particular a link between the superadditivity of the difference objective functions and the Hilbert bases of conic subpartitions in Rn