588. Forward-backward type splitting algorithms with minimal lifting II
Invited abstract in session MB-8: Systematic and computer-aided analyses I: Analyses of proximal splittings methods & friends, stream Systematic and computer-aided analyses of optimization algorithms.
Monday, 10:30-12:30Room: B100/7007
Authors (first author is the speaker)
| 1. | Emanuele Naldi
|
| Mathematics, Università di Genova | |
| 2. | Anton Åkerman
|
| Department of Automatic Control, Lund University | |
| 3. | Enis Chenchene
|
| 4. | Pontus Giselsson
|
| Dept. of Automatic Control, Lund University |
Abstract
Using the general algorithm introduced in the first part that characterize all frugal, minimally lifted and averaged nonexpansive splitting algorithms, we show that many minimal lifting splitting schemes present in the literature are incorporated in our framework. We further demonstrate how our formulation can be used to systematically design new algorithms with provable convergence guarantees and that are efficient. In order to facilitate the use of the algorithms and the choice of the involved matrices and parameters, we propose several heuristics with clear practical indications. We finally explore the application of our methods to distributed optimization, where the inherent structural properties of our framework enable efficient decentralized implementations. We conclude with numerical experiments that highlight the practical performance of our proposed methods and heuristics, illustrating competitive convergence behavior on both centralized and distributed problem instances. These results confirm the potential of our approach in a variety of large-scale optimization scenarios.
Keywords
- Large-scale optimization
- Monotone inclusion problems
Status: accepted
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