Giorgio Ottaviani

The Euclidean distance degree of orthogonally invariant matrix varieties

  • Dmitriy Drusvyatskiy
  • Hon-Leung Lee
  • Giorgio Ottaviani
  • Rekha R. Thomas
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    The Euclidean distance degree of a real variety is an important invariant arising in distance minimization problems. We show that the Euclidean distance degree of an orthogonally invariant matrix variety equals the Euclidean distance degree of its restriction to diagonal matrices. We illustrate how this result can greatly simplify calculations in concrete circumstances. Article Download … Read more

    The Euclidean distance degree of an algebraic variety

  • Jan Draisma
  • Emil Horobet
  • Giorgio Ottaviani
  • Bernd Sturmfels
  • Rekha R. Thomas
    • Categories Constrained Nonlinear Optimization, Unconstrained Optimization Tags , , ,

    The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest point maps from the perspective of computational … Read more