Abstract
There is a broad class of geometric optimization problems in R n associated with minimizing “mixed volumes” of polar bodies. In this note, we compute the point (of duality) of a planar convex figure that minimizes the length (perimeter) of its polar set. This point was first described by W. Blaschke and then later investigated by F. Steinhardt, W. Firey, E. Lutwak, and others. The algorithm is illustrated for a few examples.
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