Heinz Bauschke

The kernel average for two convex functions and its application to the extension and representation of monotone operators

  • Heinz Bauschke
  • Xianfu Wang
    • Categories Convex Optimization Tags , , , , , , , , ,

    We provide and analyze a based average for two convex functions, based on a kernel function. It covers several known averages such as the arithmetic average, epigraphical average, and the proximal average. When applied to the Fitzpatrick function and the conjugate of Fitzpatrick function associated with a monotone operator, our average produces an autoconjugate (also … Read more

    Joint minimization with alternating Bregman proximity operators

  • Heinz Bauschke
  • Patrick L. Combettes
  • Dominikus Noll
    • Categories Convex Optimization Tags , , , , , , , ,

    A systematic study of the proximity properties of Bregman distances is carried out. This investigation leads to the introduction of a new type of proximity operator which complements the usual Bregman proximity operator. We establish key properties of these operators and utilize them to devise a new alternating procedure for solving a broad class of … Read more

    The method of reflection-projection for convex feasibility problems with an obtuse cone

  • Heinz Bauschke
  • Serge Kruk
    • Categories Convex Optimization, Linear Programming Tags , , ,

    The convex feasibility problem asks to find a point in the intersection of finitely many closed convex sets in Euclidean space. This problem is of fundamental importance in mathematics and physical sciences, and it can be solved algorithmically by the classical method of cyclic projections. In this paper, the case where one of the constraints … Read more