On the symmetry function of a convex set

  title={On the symmetry function of a convex set},
  author={Alexandre Belloni and Robert M. Freund},
  journal={Math. Program.},
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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Showing 1-10 of 32 references

The Integral of a Symmetric Unimodal Function, Proc

  • T. W. Anderson
  • Amer. Math. Soc., 6, 170-176,
  • 1955
Highly Influential
4 Excerpts

Extremum problems with inequalities as subsidiary conditions, in Studies and Essays, Presented to R

  • F. John
  • Courant on His 60th Birthday, Interscience, New…
  • 1948
Highly Influential
13 Excerpts

Allegemeine Lehzätze über konvexe Polyeder, Ges

  • H. Minkowski
  • Abh., Vol.2, pp 103-121, Leipzog-Berlin,
  • 1911
Highly Influential
8 Excerpts

Measures of Symmetry for Convex Sets, in Convexity

  • B. Grünbaum
  • Proceedings of Symposia in Pure Mathematics
  • 1963
Highly Influential
4 Excerpts

Gilbert, C

  • J. F. Bonnans, J. Ch
  • Lemaréchal, and C. Sagastizábal,Numerical…
  • 2003
1 Excerpt

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