# About Lagrangian Methods in Integer Optimization

Frangioni, Antonio (2004) About Lagrangian Methods in Integer Optimization. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

## 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 \emph{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.

Item Type: Book Lagrangian dual, Integer Linear Programs. Area01 - Scienze matematiche e informatiche > INF/01 - Informatica Dipartimenti (until 2012) > DIPARTIMENTO DI INFORMATICA dott.ssa Sandra Faita 10 Dec 2014 09:36 10 Dec 2014 09:36 http://eprints.adm.unipi.it/id/eprint/2119

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