Minimising the number of faces of a class of polytopes

Abstract: Polytopes are the natural domains of many optimisation problems. We consider a ``higher order" optimisation problem, whose domain is a class of polytopes, asking what is the minimum number of faces (of a given dimension) for this class, and which polytopes are the minimisers. Generally we consider the class of d-dimensional polytopes with V vertices, for fixed V and d. The corresponding maximisation problem was solved decades ago, but serious progress on the minimisation question has only been made in recent years.

optimization and control

Audience: researchers in the topic

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