Letter to the Editor—A Note on the Generalized Lagrange Multiplier Solution to an Integer Programming Problem

George L. Nemhauser and Zev Ullmann
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George L. Nemhauser: The Johns Hopkins University, Baltimore, Maryland
Zev Ullmann: The Johns Hopkins University, Baltimore, Maryland

Operations Research, 1968, vol. 16, issue 2, 450-453

Abstract: The problem of applying Generalized Lagrange Multipliers (GLM) to 0-1 integer programming problems is investigated. It is shown that GLM can produce optimal solutions if and only if these solutions are extreme points of the convex set of linear equations. The presentation is based on a capital allocation problem recently discussed by Kaplan. Kaplan's procedure for finding optimal solutions that are not extreme points is discussed in terms of linear programming.

Date: 1968
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