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Abstract: In this paper we consider the solution of certain convex integer minimizationproblems via greedy augmentation procedures. We show that a greedy augmentationprocedure that employs only directions from certain Graver bases needs onlypolynomially many augmentation steps to solve the given problem. We extendthese results to convex $N$-fold integer minimization problems and to convex2-stage stochastic integer minimization problems. Finally, we present someapplications of convex $N$-fold integer minimization problems for which ourapproach provides polynomial time solution algorithms.



Autor: Raymond Hemmecke, Shmuel Onn, Robert Weismantel

Fuente: https://arxiv.org/







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