Christopher Hendrich

A Douglas-Rachford type primal-dual method for solving inclusions with mixtures of composite and parallel-sum type monotone operators

  • Radu Ioan Bot
  • Christopher Hendrich
    • Categories Convex Optimization Tags , , ,

    In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, however applied in different underlying Hilbert spaces. Most importantly, the algorithms allow to process the bounded linear operators and the set-valued operators occurring in the … Read more

    Convergence analysis for a primal-dual monotone + skew splitting algorithm with applications to total variation minimization

  • Radu Ioan Bot
  • Christopher Hendrich
    • Categories Convex Optimization Tags , , ,

    In this paper we investigate the convergence behavior of a primal-dual splitting method for solving monotone inclusions involving mixtures of composite, Lipschitzian and parallel sum type operators proposed by Combettes and Pesquet in [7]. Firstly, in the particular case of convex minimization problems, we derive convergence rates for the sequence of objective function values by … Read more

    A variable smoothing algorithm for solving convex optimization problems

  • Radu Ioan Bot
  • Christopher Hendrich
    • Categories Applications - Science and Engineering, Convex Optimization, Data-Mining Tags , , ,

    In this article we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth the latter to a convex and differentiable function with Lipschitz continuous gradient by using both variable and constant smoothing parameters. … Read more