variable metric method

Unifying abstract inexact convergence theorems and block coordinate variable metric iPiano

  • Peter Ochs
    • Categories Nonsmooth Optimization Tags , , , , , , , , ,

    An abstract convergence theorem for a class of generalized descent methods that explicitly models relative errors is proved. The convergence theorem generalizes and unifies several recent abstract convergence theorems. It is applicable to possibly non-smooth and non-convex lower semi-continuous functions that satisfy the Kurdyka–Lojasiewicz (KL) inequality, which comprises a huge class of problems. Most of … Read more

    An extension of the projected gradient method to a Banach space setting with application in structural topology optimization

  • Luise Blank
  • Christoph Rupprecht
    • Categories Constrained Nonlinear Optimization, Control Applications, Systems governed by Differential Equations Optimization Tags , , , ,

    For the minimization of a nonlinear cost functional under convex constraints the relaxed projected gradient process is a well known method. The analysis is classically performed in a Hilbert space. We generalize this method to functionals which are differentiable in a Banach space. The search direction is calculated by a quadratic approximation of the cost … Read more