About Lagrangian Methods in Integer Optimization

Antonio Frangioni ()

Annals of Operations Research, 2005, vol. 139, issue 1, 163-193

Abstract: It is well-known that the Lagrangian dual of an Integer Linear Program (ILP) provides the same bound as a continuous relaxation involving the convex hull of all the optimal solutions of the Lagrangian relaxation. It is less often realized that this equivalence is effective, in that basically all known algorithms for solving the Lagrangian dual either naturally compute an (approximate) optimal solution of the “convexified relaxation”, or can be modified to do so. After recalling these results we elaborate on the importance of the availability of primal information produced by the Lagrangian dual within both exact and approximate approaches to the original (ILP), using three optimization problems with different structure to illustrate some of the main points. Copyright Springer Science + Business Media, Inc. 2005

Keywords: Lagrangian dual; integer linear programs (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (14)

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DOI: 10.1007/s10479-005-3447-9

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