Technical Note—On the Generalized Lattice Point Problem and Nonlinear Programming

Abstract

In this paper we consider a problem that is equivalent to the generalized lattice point problem of nonconvex programming. This problem can be expressed as the maximization of a certain convex function over a convex polyhedral set. This formulation can be used with the cutting plane algorithm of Glover and Klingman sometimes to strengthen the cuts their method generates for the generalized lattice point problem. A cut for zero-one integer programming can also be derived.