ellipsoid algorithm

An Oblivious Ellipsoid Algorithm for Solving a System of (In)Feasible Linear Inequalities

  • Robert M. Freund
  • Michael J. Todd
  • Jourdain Lamperski
    • Categories Convex Optimization, Linear Programming, Nonsmooth Optimization Tags , , , ,

    The ellipsoid algorithm is a fundamental algorithm for computing a solution to the system of m linear inequalities in n variables (P) when its set of solutions has positive volume. However, when (P) is infeasible, the ellipsoid algorithm has no mechanism for proving that (P) is infeasible. This is in contrast to the other two … Read more

    Equivalence of Convex Problem Geometry and Computational Complexity in the Separation Oracle Model

  • Robert M. Freund
  • Jorge Vera
    • Categories Convex Optimization Tags , , , ,

    Consider the following supposedly-simple problem: “compute x \in S” where S is a convex set conveyed by a separation oracle, with no further information (e.g., no bounding ball containing or intersecting S, etc.). Our interest in this problem stems from fundamental issues involving the interplay of computational complexity, the geometry of S, and the stability … Read more