fenchel duality

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

    Deriving robust counterparts of nonlinear uncertain inequalities

  • Aharon Ben-Tal
  • Dick den Hertog
  • Jean-Philippe Vial
    • Categories Constrained Nonlinear Optimization, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , , , ,

    In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It … Read more