133. Krasnoselskii-Mann Iterations: Inertia, Perturbations and Approximation
Invited abstract in session FB-4: Large-scale optimization II, stream Large-scale optimization.
Friday, 10:05 - 11:20Room: M:M
Authors (first author is the speaker)
| 1. | Daniel Cortild
|
| Faculty of Science and Engineering, University of Groningen | |
| 2. | Juan Peypouquet
|
| Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen |
Abstract
Krasnoselskii-Mann iterations constitute a class of fixed point iterations combined with relaxations, employed to approximate fixed points of (quasi-)nonexpansive operators. We present a study of a family of such iterations combining different inertial principles into a single framework. 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 that these methods are robust with respect to different kinds of perturbations--which may come from computational errors, intentional deviations, as well as regularisation or approximation schemes--under surprisingly weak assumptions on the magnitude of the perturbations. Although we mostly focus on theoretical aspects, a numerical illustration based on the image inpainting problem reveals possible trends in the behaviour of these types of methods.
The talk is based on joint work with Juan Peypouquet.
Keywords
- Convex and non-smooth optimization
- Large- and Huge-scale optimization
Status: accepted
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