Tag Archives: convex geometry

Brunn-Minkowski, Prékopa-Leindler, and isoperimetry

Found a great overview of the subject with a lot of insight. Another brief intro is here.

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‘Shear’ convex polyhedra: solution

Here I describe the solution to the problem from the last post. Spoilers!

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‘Shear’ convex polyhedra

I came up with what seems quite a beautiful geometric construction solving the problem described below. On a compact convex set    consider the function where we denote  In other words, “hanging” in the point    we measure the “width” of the … Continue reading

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Projection on a convex set is closer to any point of the set

A useful little fact for constrained optimization. Let    be a convex set, and consider      and its projection on   As quickly follows from the separation theorem with hyperplane containing  for any    the angle between    and    is obtuse. … Continue reading

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