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

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 op...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 195; H. 1; S. 205 - 225
Hauptverfasser: Briceño-Arias, Luis M., Roldán, Fernando
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.10.2022
Springer Nature B.V
Schlagworte:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Computational geometry
Convex analysis
Convexity
Engineering
Game theory
Hilbert space
Hypotheses
Inclusions
Mathematics
Mathematics and Statistics
Methods
Operations Research/Decision Theory
Operators (mathematics)
Optimization
Partial differential equations
Searching
Splitting
Theory of Computation
Lipschitzian operator
47H10
65K15
65K05
Convex optimization
Monotone operator theory
Splitting algorithms
90C25
49M29
Cocoercive operator
47H05
ISSN:0022-3239, 1573-2878
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Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-022-02074-3