Yurii Nesterov

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

    Augmented self-concordant barriers and nonlinear optimization problems with finite complexity.

  • Yurii Nesterov
  • Jean-Philippe Vial
    • Categories Integer Programming Tags , ,

    In this paper we study special barrier functions for the convex cones, which are the sum of a self-concordant barrier for the cone and a positive-semidefinite quadratic form. We show that the central path of these augmented barrier functions can be traced with linear speed. We also study the complexity of finding the analytic center … Read more

    Augmented self concordant barriers and nonlinear optimization problems with finite complexity

  • Yurii Nesterov
  • Jean-Philippe Vial
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    In this paper we study special barrier functions for the convex cones, which are the sum of a self-concordant barrier for the cone and a positive-semidefinite quadratic form. We show that the central path of these augmented barrier functions can be traced with linear speed. We also study the complexity of finding the analytic center … Read more