Cone Programming

Automorphisms of rank-one generated hyperbolicity cones and their derivative relaxations

  • Masaru Ito
  • Bruno F. Lourenço
    • Categories Cone Programming, Linear, Cone and Semidefinite Programming Tags , ,

    A hyperbolicity cone is said to be rank-one generated (ROG) if all its extreme rays have rank one, where the rank is computed with respect the underlying hyperbolic polynomial. This is a natural class of hyperbolicity cones which are strictly more general than the ROG spectrahedral cones. In this work, we present a study of … Read more

    On duality theory of conic linear problems

  • Alexander Shapiro
    • Categories Cone Programming, Convex Optimization, Infinite Dimensional Optimization

    In this paper we discuss duality theory of optimization problems with a linear objective function and subject to linear constraints with cone inclusions, referred to as conic linear problems. We formulate the Lagrangian dual of a conic linear problem and survey some results based on the conjugate duality approach where the questions of “no duality … Read more