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Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes

2 votes
Accepted

Closed form solutions for maximal subsets of convex polytopes

By Ivan's request, I describe here two algorithms for finding the maximum-size ball contained in a given $n$-dimensional convex polytope $P$. The first algorithm, requiring central symmetry of $P$, pr …
Wlodek Kuperberg's user avatar
17 votes

How to make a sandwich from just one piece of bread?

This won't be a complete answer to Q2, but something of a starting point, at least for all two-dimensional convex $P$. Assuming for simplicity that the area of $P$ is 1, $P$ contains a parallelogram o …
Wlodek Kuperberg's user avatar