Article ID: | iaor2006990 |
Country: | Netherlands |
Volume: | 139 |
Issue: | 1 |
Start Page Number: | 163 |
End Page Number: | 193 |
Publication Date: | Oct 2005 |
Journal: | Annals of Operations Research |
Authors: | Frangioni Antonio |
Keywords: | Lagrangian methods, duality |
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.