Papers › On Finding the Closest Zonotope to a Polytope in Hausdorff Distance
On Finding the Closest Zonotope to a Polytope in Hausdorff Distance
George D. Torres
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We provide a local theory for the optimization of the Hausdorff distance between a polytope and a zonotope. To do this, we compute explicit local formulae for the Hausdorff function d(P, -) : Zₙ →ℝ, where P is a fixed polytope and Zₙ is the space of rank n zonotopes. This local theory is then used to provide an optimization algorithm based on subgradient descent that converges to critical points of d(P, -). We also express the condition of being at a local minimum as a polyhedral feasibility condition.
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