361. Forward-backward algorithms devised by graphs
Invited abstract in session TB-9: Variational Analysis I, stream Variational analysis: theory and algorithms.
Tuesday, 10:30-12:30Room: B100/8013
Authors (first author is the speaker)
| 1. | Francisco Javier Aragón Artacho
|
| Mathematics, University of Alicante | |
| 2. | Rubén Campoy
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| Department of Mathematics, Universidad de Alicante | |
| 3. | César López Pastor
|
| Mathematics, Universidad de Alicante |
Abstract
In this talk, we will present a methodology for devising forward-backward methods for finding zeros in the sum of a finite number of maximally monotone operators. We extend the techniques from [SIAM J. Optim., 34 (2024), pp. 1569-1594] to cover the case involving a finite number of cocoercive operators, which should be directly evaluated by the algorithm instead of computing their resolvent. The algorithms are induced by three graphs that determine how the algorithm variables interact with each other and how they are combined to compute each resolvent. The hypotheses on these graphs ensure that the algorithms obtained have minimal lifting and are frugal, meaning that the ambient space of the underlying fixed point operator has minimal dimension and that each resolvent and each cocoercive operator is evaluated only once per iteration. This framework not only allows to recover some known methods, but also to generate new ones, as the forward-backward algorithm induced by a complete graph. If time permits, we will present some numerical experiments showing how the choice of graphs influences the performance of the algorithms.
Keywords
- Computational mathematical optimization
- Non-smooth optimization
- Monotone inclusion problems
Status: accepted
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