Generalized Lagrange Multipliers in Integer Programming

This paper combines the theory of generalized Lagrange multipliers with a reformulation of the integer-programming problem due to group theory. The use of multipliers enhances the algorithmic efficiency of group theory in a variety of ways. One particular application is the approximation of generalized Lagrange multipliers by generalized linear programming as suggested by Brooks and Geoffrion. This procedure is shown to be closely related to the cutting-plane method of Gomory.