On the symmetry function of a convex set

Abstract. 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{ 0 : x + (x - y) S for every y S} , which essentially measures how symmetric S is about the point x, and define sym(S) := max xS sym(x, S) ; x is called a symmetry point of S if x achieves the above maximum. The set S is a symmetric

• Type: Journal
• Year: 2008
• Where: MP
• Authors: Alexandre Belloni, Robert M. Freund
• Keywords: Broad Exploration, MP 2008, Symmetry, Symmetry Function