support function

CONVEX GEOMETRY OF THE GENERALIZED MATRIX-FRACTIONAL FUNCTION

  • James V. Burke
  • Tim Hoheisel
  • Yuan Gao
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , ,

    Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems, regularization and learning. In this paper we dramatically simplify the support function representation for GMF functions as well as the representation of … Read more

    On a new class of matrix support functionals with applications

  • James V. Burke
  • Tim Hoheisel
    • Categories Convex and Nonsmooth Optimization, Quadratic Programming, Semi-definite Programming Tags , , , , , ,

    A new class of matrix support functionals is presented which establish a connection between optimal value functions for quadratic optimization problems, the matrix-fractional function, the pseudo matrix-fractional function, and the nuclear norm. The support function is based on the graph of the product of a matrix with its transpose. Closed form expressions for the support … Read more