Nonlinear Forward-Backward Splitting with Momentum Correction [article]

Martin Morin, Sebastian Banert, Pontus Giselsson
2022 arXiv   pre-print
The nonlinear, or warped, resolvent recently explored by Giselsson and B\'ui-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
more » ... wide range of special cases. These cases cover and expand on the forward-reflected-backward method of Malitsky-Tam, the primal-dual methods of V\~u-Condat and Chambolle-Pock, and the forward-reflected-Douglas-Rachford method of Ryu-V\~u. A new primal-dual method that uses an extra resolvent step is also presented as well as a general approach for adding Polyak momentum to any special case of our nonlinear forward-backward method, in particular all the algorithms listed above.
arXiv:2112.00481v3 fatcat:ma6vpct6qfgsfpz36gtyg2kqyq