Generalizing 0-1 conflict hypergraphs and mixed conflict graphs: mixed conflict hypergraphs in discrete optimization

Abstract

This work starts a new level of research in the area of conflict graphs and hypergraphs. We introduce a new term “mixed conflict hypergraphs”, which comes from merging and generalizing 0-1 conflict hypergraphs and mixed conflict graphs. Two structured mixed integer problems (referred to as convexification of posynomial and signomial functions, CoPF and CoSF, respectively) are solved efficiently with applying new strong cutting planes, outperforming modern commercial software.