symmetry

Projective Pre-Conditioners for Improving the Behavior of a Homogeneous Conic Linear System

  • Alexandre Belloni
  • Robert M. Freund
    • Categories Linear, Cone and Semidefinite Programming Tags , , , , ,

    We present a general theory for transforming a homogeneous conic system F: Ax = 0, x \in C, x \ne 0, to an equivalent system via projective transformation induced by the choice of a point in a related dual set. Such a projective transformation serves to pre-condition the conic system into a system that has … Read more

    Symmetry Points of Convex Set: Basic Properties and Computational Complexity

  • Alexandre Belloni
  • Robert M. Freund
    • Categories Convex and Nonsmooth Optimization, Linear Programming Tags , , ,

    Given a convex body S and a point x \in S, let sym(x,S) denote the symmetry value of x in S: sym(x,S):= max{t : x + t(x – y) \in S for every y \in S}, which essentially measures how symmetric S is about the point x, and define sym(S):=\max{sym(x,S) : x \in S }. … Read more