Report of the Session on Polyhedral Aspects of Discrete Optimization

Abstract

Publisher Summary The “linear discrete optimization problem” is the problem of maximizing a linear objective function cx over a finite set S. For any such finite set there exists a unique bounded polyhedron P, which contains S, and whose vertices are a subset of S. This polyhedron is called the convex hull of S. Every such polyhedron can be alternatively defined as the solution set of a finite system L of linear inequalities. Because the optimal solution to an optimization problem where one maximizes a linear function over a polyhedral set occurs at a vertex of that polyhedron, one could solve the discrete optimization problem by maximizing cx over the solution set of L using linear programming techniques. These observations motivated extensive research efforts directed to characterizing and investigating the facial structure of the polyhedron associated with a given discrete optimization problem. A systematic way is required to generate the system of linear inequalities L, or equivalently if all facets of P can be produced, then a discrete optimization problem can be replaced by its equivalent linear programming problem.