riemannian geometry

On the Central Paths and Cauchy Trajectories in Semidefinite Programming

  • Julio López
  • Héctor Ramírez
    • Categories Semi-definite Programming Tags , , , ,

    In this work, we study the properties of central paths, defined with respect to a large class of penalty and barrier functions, for convex semidefinite programs. The type of programs studied here is characterized by the minimization of a smooth and convex objective function subject to a linear matrix inequality constraint. So, it is a … Read more

    On the Riemannian Geometry Defined by Self-Concordant Barriers and Interior-Point Methods

  • Yurii Nesterov
  • Michael J. Todd
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , ,

    We consider the Riemannian geometry defined on a convex set by the Hessian of a self-concordant barrier function, and its associated geodesic curves. These provide guidance for the construction of efficient interior-point methods for optimizing a linear function over the intersection of the set with an affine manifold. We show that algorithms that follow the … Read more