Four-Operator Splitting via a Forward–Backward–Half-Forward Algorithm with Line Search

Luis M. Briceño-Arias () and Fernando Roldán ()
Additional contact information
Luis M. Briceño-Arias: Universidad Técnica Federico Santa María
Fernando Roldán: Universidad Técnica Federico Santa María

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 1, No 8, 205-225

Abstract: Abstract In this article, we provide a splitting method for solving monotone inclusions in a real Hilbert space involving four operators: a maximally monotone, a monotone-Lipschitzian, a cocoercive, and a monotone-continuous operator. The proposed method takes advantage of the intrinsic properties of each operator, generalizing the forward–backward–half-forward splitting and the Tseng’s algorithm with line search. At each iteration, our algorithm defines the step size by using a line search in which the monotone-Lipschitzian and the cocoercive operators need only one activation. We also derive a method for solving nonlinearly constrained composite convex optimization problems in real Hilbert spaces. Finally, we implement our algorithm in a nonlinearly constrained least-square problem and we compare its performance with available methods in the literature.

Keywords: Convex optimization; Cocoercive operator; Lipschitzian operator; Monotone operator theory; Splitting algorithms; 47H05; 47H10; 65K05; 65K15; 90C25; 49M29 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-022-02074-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:195:y:2022:i:1:d:10.1007_s10957-022-02074-3

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-022-02074-3

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().