In the past 5 years advances in algebraic-geometric algorithms have been used to prove unexpected new results on the computation of non-linear integer programs. These lectures will introduce the audience to new techniques. I will describe several algorithms and explain why we can now prove theorems that were beyond our reach before, mostly about integer optimization with non-linear objectives. I will also describe attempts to turn these two algorithms into practical computation, not just in theoretical results.
This a nice story collecting results by various authors and now contained in our monograph recently published by SIAM-MOS.
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