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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Hemmecke, R., Onn, S. & Weismantel, R. A polynomial oracle-time algorithm for convex integer minimization. Math. Program. 126, 97–117 (2011). https://doi.org/10.1007/s10107-009-0276-7
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DOI: https://doi.org/10.1007/s10107-009-0276-7