Guillaume Garrigos

Splitting methods with variable metric for KL functions

  • Pierre Frankel
  • Juan Peypouquet
  • Guillaume Garrigos
    • Categories Nonsmooth Optimization, Other Topics

    We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satis es the Kurdyka-Lojasiewicz inequality in a Hilbert space. We prove that any precompact sequence converges to a critical point of f and obtain new convergence rates both for the values and the iterates. The analysis covers alternating … Read more

    A dynamic gradient approach to Pareto optimization with nonsmooth nonconvex objective functions

  • Hédy Attouch
  • Guillaume Garrigos
  • Xavier Goudou
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization

    In a general Hilbert framework, we consider continuous gradient-like dynamical systems for constrained multiobjective optimization involving non-smooth convex objective functions. Our approach is in the line of a previous work where was considered the case of convex di erentiable objective functions. Based on the Yosida regularization of the subdi erential operators involved in the system, we obtain … Read more