The bundle method for hard combinatorial optimization problems

Authors:
Gerald Gruber;Franz Rendl
Affiliations:
Carinthia Tech Institute, School of Geoinformation, A-9524 Villach, Austria;University of Klagenfurt, Department of Mathematics, A-9020 Klagenfurt, Austria
Venue:
Combinatorial optimization - Eureka, you shrink!
Year:
2003

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Abstract

Solving the well known relaxations for large scale combinatorial optimization problems directly is out of reach. We use Lagrangian relaxations and solve it with the bundle method. The cutting plane model at each iteration which approximates the original problem can be kept moderately small and we can solve it very quickly. We report successful numerical results for approximating maximum cut.