We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Extragradient-type methods with O1/k last-iterate convergence rates for co-hypomonotone inclusions.
- Authors
Tran-Dinh, Quoc
- Abstract
We develop two "Nesterov's accelerated" variants of the well-known extragradient method to approximate a solution of a co-hypomonotone inclusion constituted by the sum of two operators, where one is Lipschitz continuous and the other is possibly multivalued. The first scheme can be viewed as an accelerated variant of Tseng's forward-backward-forward splitting (FBFS) method, while the second one is a Nesterov's accelerated variant of the "past" FBFS scheme, which requires only one evaluation of the Lipschitz operator and one resolvent of the multivalued mapping. Under appropriate conditions on the parameters, we theoretically prove that both algorithms achieve O 1 / k last-iterate convergence rates on the residual norm, where k is the iteration counter. Our results can be viewed as alternatives of a recent class of Halpern-type methods for root-finding problems. For comparison, we also provide a new convergence analysis of the two recent extra-anchored gradient-type methods for solving co-hypomonotone inclusions.
- Subjects
SET-valued maps; RESOLVENTS (Mathematics)
- Publication
Journal of Global Optimization, 2024, Vol 89, Issue 1, p197
- ISSN
0925-5001
- Publication type
Article
- DOI
10.1007/s10898-023-01347-z