A polynomial oracle-time algorithm for convex integer minimization

Details A polynomial oracle-time algorithm for convex integer minimization A polynomial oracle-time algorithm for convex integer minimization

2007-10-16

arxiv.org/abs/0710.3003v1

Mathematical Programming: Volume 126, Issue 1 (2011), Page 97-117

Mathematics

Optimization and Control

19 pages, 1 figure

Scientific paper

10.1007/s10107-009-0276-7

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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