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

George L. Nemhauser | Zendy; Zev Ullmann | Zendy

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

Author(s) -

George L. Nemhauser,

Zev Ullmann

Publication year - 1968

Publication title -

operations research

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.797

H-Index - 140

eISSN - 1526-5463

pISSN - 0030-364X

DOI - 10.1287/opre.16.2.450

Subject(s) - lagrange multiplier , integer programming , extreme point , mathematical optimization , mathematics , linear programming , multiplier (economics) , integer (computer science) , branch and price , set (abstract data type) , computer science , combinatorics , economics , programming language , macroeconomics

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.

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