Juan Peypouquet

Krasnoselskii-Mann Iterations: Inertia, Perturbations and Approximation

  • Daniel Cortild
  • Juan Peypouquet
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization Tags , , ,

    This paper is concerned with the study of a family of fixed point iterations combining relaxation with different inertial (acceleration) principles. We provide a systematic, unified and insightful analysis of the hypotheses that ensure their weak, strong and linear convergence, either matching or improving previous results obtained by analysing particular cases separately. We also show … Read more

    Inertial Krasnoselskii-Mann Iterations

  • Juan Peypouquet
    • Categories Convex Optimization, Other Topics

    We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with worst case estimates for the rate at which the residuals vanish. Strong and linear convergence are obtained in the quasi-contractive setting. In both cases, we highlight the relationship with the non-inertial case, and … Read more