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arXiv · 0710.3003

A polynomial oracle-time algorithm for convex integer minimization

Raymond Hemmecke·Shmuel Onn·Robert Weismantel
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Abstract

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex $N$-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex $N$-fold integer minimization problems for which our approach provides polynomial time solution algorithms.

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Raymond Hemmecke, Shmuel Onn, Robert Weismantel. 2007-10-16. A polynomial oracle-time algorithm for convex integer minimization. https://doi.org/10.1007/s10107-009-0276-7

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