171. On the Bredies-Chenchene-Lorenz-Naldi algorithm
Invited abstract in session WF-7: Regularization methods for Machine Learning and Inverse Problems, stream Optimization for Inverse Problems and Machine Learning.
Wednesday, 16:20 - 18:00Room: M:I
Authors (first author is the speaker)
| 1. | Shambhavi Singh
|
| Combinatorics and Optimization, University of Waterloo |
Abstract
Monotone inclusion problems occur in many areas of optimization and variational analysis. Splitting methods, which utilize resolvents or proximal mappings of the underlying operators, are often applied to solve these problems. In 2022, Bredies, Chenchene, Lorenz, and Naldi introduced a new elegant algorithmic framework that encompasses various well known algorithms including Douglas-Rachford and Chambolle-Pock. They obtained powerful weak and strong convergence results, where the latter type relies on additional strong monotonicity assumptions. In this paper, we complement the analysis by Bredies et al. by relating the projections of the fixed point sets of the underlying operators that generate the (reduced and original) preconditioned proximal point sequences. We also obtain strong convergence results in the case of linear relations. Various examples are provided to illustrate the applicability of our results.
Keywords
- Convex and non-smooth optimization
- Linear and nonlinear optimization
Status: accepted
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