convex geometry

Optimal switching sequence for switched linear systems

  • Qie He
  • Zeyang Wu
    • Categories Combinatorial Optimization, Control Applications, Dynamic Programming Tags , , , , ,

    We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of n-by-n matrices and an n-dimensional vector, find a sequence of K matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the K matrices and the … 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