AbstractWe consider the integer points in a unimodular cone K ordered by a lexicographic rule defined by a lattice basis. To each integer point x in K we associate a family of inequalities (lex-inequalities) that define the convex hull of the integer points in K that are not lexicographically smaller than x. The family of lex-inequalities contains the Chvátal–Gomory cuts, but does not contain and is not contained in the family of split cuts. This provides a finite cutting plane method to solve the integer program $$\min \{cx: x\in S\cap \mathbb {Z}^n\}$$
min
{
c
x
:
x
∈
S
∩
Z
n
}
, where $$S\subset \mathbb {R}^n$$
S
⊂
R
n
is a compact set and $$c\in \mathbb {Z}^n$$
c
∈
Z
n
. We analyze the number of iterations of our algorithm.
Integer points close to convex surfaces
