Nonlinear Forward-Backward Splitting with Momentum Correction

Martin Morin, Sebastian Banert, Pontus Giselsson

Research output: Contribution to journalArticlepeer-review

Abstract

The nonlinear, or warped, resolvent recently explored by Giselsson and Bùi-Combettes has been used to model a large set of existing and new monotone inclusion algorithms. To establish convergent algorithms based on these resolvents, corrective projection steps are utilized in both works. We present a different way of ensuring convergence by means of a nonlinear momentum term, which in many cases leads to cheaper per-iteration cost. The expressiveness of our method is demonstrated by deriving a wide range of special cases. These cases cover and expand on the forward-reflected-backward method of Malitsky-Tam, the primal-dual methods of Vũ-Condat and Chambolle-Pock, and the forward-reflected-Douglas-Rachford method of Ryu-Vũ. A new primal-dual method that uses an extra resolvent step is also presented as well as a general approach for adding momentum to any special case of our nonlinear forward-backward method, in particular all the algorithms listed above.

Original languageEnglish
Article number37
JournalSet-Valued and Variational Analysis
Volume31
Issue number4
DOIs
Publication statusPublished - 2023

Subject classification (UKÄ)

  • Control Engineering

Free keywords

  • Forward-backward splitting
  • Forward-reflected-backward splitting
  • Four-operator splitting
  • Momentum
  • Monotone inclusions
  • Nonlinear resolvent
  • Primal-dual splitting

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