univariate polynomial matrices

Generalized Ellipsoids

  • Abraar Chaudhry
  • Amir Ali Ahmadi
  • Cemil Dibek
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    We introduce a family of symmetric convex bodies called generalized ellipsoids of degree \(d\) (GE-\(d\)s), with ellipsoids corresponding to the case of \(d=0\). Generalized ellipsoids (GEs) retain many geometric, algebraic, and algorithmic properties of ellipsoids. We show that the conditions that the parameters of a GE must satisfy can be checked in strongly polynomial time, … Read more

    Time-Varying Semidefinite Programs

  • Amir Ali Ahmadi
  • Bachir El Khadir
    • Categories Basic Sciences Applications, Infinite Dimensional Optimization, Semi-definite Programming Tags , , , , ,

    We study time-varying semidefinite programs (TV-SDPs), which are semidefinite programs whose data (and solutions) are functions of time. Our focus is on the setting where the data varies polynomially with time. We show that under a strict feasibility assumption, restricting the solutions to also be polynomial functions of time does not change the optimal value … Read more