On the symmetry function of a convex set

@article{Belloni2008OnTS,
  title={On the symmetry function of a convex set},
  author={Alexandre Belloni and Robert M. Freund},
  journal={Math. Program.},
  year={2008},
  volume={111},
  pages={57-93}
}
We attempt a broad exploration of properties and connections between the symmetry function of a convex set S ⊂ IRn and other arenas of convexity including convex functions, convex geometry, probability theory on convex sets, and computational complexity. Given a point x ∈ S, let sym(x, S) denote the symmetry value of x in S: sym(x, S) := max{α ≥ 0 : x + α(x − y) ∈ S for every y ∈ S} , which essentially measures how symmetric S is about the point x, and define sym(S) := max x∈S sym(x, S) ; x∗ is… CONTINUE READING

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