Institution: Stanford University, Department of Computer Science

Title: Integer programming over a cone

Author: Pnueli, Amir

Date: July 1968

Abstract: The properties of a special form integer programming problem are discussed. We restrict ourselves to optimization over a cone (a set of n constraints in n unconstrained variables) with a square matrix of positive diagonal and non positive off-diagonal elements. (Called a bounding form by F. Glover [1964]). It is shown that a simple iterational process gives the optimal integer solution in a finite number of steps. It is then shown that any cone problem with bounded rational solution can be transformed to the bounding form and hence solved by the outlined method. Some extensions to more than n constraints are discussed and a numerical example is shown to solve a bigger problem.

http://i.stanford.edu/pub/cstr/reports/cs/tr/68/102/CS-TR-68-102.pdf