Set characterizations and convex extensions for geometric convex-hull proofs

In the present work, we consider Zuckerberg's method for geometric convex-hull proofs introduced in [Geometric convex hull defining formulations, Operations Research Letters 44(5), 625-629 (2016)]. It has only been scarcely adopted literature so far, despite great flexibility designing algorithmic completeness of polyhedral descriptions that it offers. We suspect this is partly due to rather heavy algebraic framework its original statement entails. This why a much more lightweight and accessible approach proof technique, building on ideas from [Extended formulations hulls some bilinear functions, Discrete Optimization 36, 100569 (2020)]. introduce concept set characterizations replace set-theoretic expressions needed version facilitate construction schemes. Along with this, develop several different strategies conduct Zuckerberg-type proofs. Very importantly, also show our allows significant extension technique. While was applicable 0/1-polytopes, extended treat arbitrary polyhedra even general sets. demonstrate increase expressive power by characterizing Boolean functions over polytopal domains. All results are illustrated indicative examples underline practical usefulness wide applicability framework.