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On the Augmented Lagrangian Dual for Integer Programming

Natashia Boland (Natashia.Boland***at***newcastle.edu.au)
Andrew Eberhard (andy.eberhard***at***rmit.edu.au)

Abstract: We consider the augmented Lagrangian dual for integer programming, and provide a primal characterization of the resulting bound. As a corollary, we obtain proof that the augmented Lagrangian is a strong dual for integer programming. We are able to show that the penalty parameter applied to the augmented Lagrangian term may be placed at a fixed, large value and still obtain strong duality for pure integer programs.

Keywords: Strong Duality, Mixed Integer Programming, Augmented Lagrangian

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Citation: Report C-OPT 2013-01, The University of Newcastle, Callaghan, NSW, 2308, Australia, 2013

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Entry Submitted: 01/22/2013
Entry Accepted: 01/22/2013
Entry Last Modified: 01/26/2013

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