The article applies an approach, which was previously used by the author, to evaluate the number of extreme points in the convex hull of a set M of integer solutions for a system of linear equations. We consider the properties of extreme points for the case when M is defined by a system of linear equations and congruences, and we obtain various bounds on their number. The same is performed for a set M defined by a system of linear inequalities. For a fixed dimension value the bounds are polynomial and do not depend on the right-hand side of the systems that define M. We also show how similar problems may be treated for a partially integer case.

integer programming, convex hull, linear equation system, linear inequality system, extreme points

Mathematical problems and theory of numerical methods