Two Relaxed Inertial Forward–Reflected–Backward Splitting Algorithms With Momentum Terms

In this paper, to solve the monotone inclusion problem consisting of the sum of two monotone operators in Hilbert spaces, we propose and study two modifications of Malitsky–Tam’s forward–reflection–backward splitting methods with double momentum terms. Meanwhile, we consider a relaxed inertial versi...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Journal of Mathematics Ročník 2025; číslo 1
Hlavní autori:	Zhang, Binbin, Guan, Ximeng, Yin, Chenhao
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	John Wiley & Sons, Inc 01.01.2025 Wiley
Predmet:	Algorithms United Kingdom
ISSN:	2314-4629, 2314-4785
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Popis
Shrnutí:	In this paper, to solve the monotone inclusion problem consisting of the sum of two monotone operators in Hilbert spaces, we propose and study two modifications of Malitsky–Tam’s forward–reflection–backward splitting methods with double momentum terms. Meanwhile, we consider a relaxed inertial version to expand the range of allowable step sizes. Under the same assumptions as the Malitsky–Tam’s method (i.e., the set‐valued operator is maximally monotone, and the single‐valued operator is Lipschitz continuous and monotone), we prove the weak convergence and linear convergence of the proposed methods, respectively. Numerical results show that the relaxed inertial version effectively improves the convergence performance compared to the Malitsky–Tam’s splitting algorithm and its inertial version.
ISSN:	2314-4629 2314-4785
DOI:	10.1155/jom/7014819