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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Vydané v:	Journal of optimization theory and applications Ročník 195; číslo 1; s. 205 - 225
Hlavní autori:	Briceño-Arias, Luis M., Roldán, Fernando
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.10.2022 Springer Nature B.V
Predmet:	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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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.
AbstractList	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.
Author	Roldán, Fernando Briceño-Arias, Luis M.
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Cites_doi	10.1007/s00245-019-09597-8 10.1090/S0002-9904-1964-11178-2 10.1090/pspum/018.1/0285942 10.1137/18M1207260 10.1137/120901106 10.1137/0716071 10.1007/s10957-015-0703-2 10.1080/02331934.2012.733883 10.1007/s11228-020-00542-4 10.1007/BF01448388 10.1007/s11590-019-01509-7 10.1016/j.amc.2015.01.017 10.1007/s10444-011-9254-8 10.1287/moor.2021.1161 10.1007/s10898-020-00940-w 10.1016/S1570-579X(01)80010-0 10.1137/10081602X 10.1007/s10957-019-01601-z 10.1137/S0363012998338806 10.1016/S0168-2024(08)70034-1 10.1007/978-1-4614-7621-4_9 10.1007/978-3-319-48311-5 10.1007/s10444-018-9619-3 10.1016/j.amc.2020.125248 10.1007/s10013-015-0121-7 10.1137/120872802 10.1080/02331934.2013.855210 10.1007/s10957-017-1074-7 10.1137/16M1073741 10.1007/s10107-016-1044-0 10.1007/978-0-8176-4848-0 10.1137/17M1120099 10.1090/surv/049 10.1007/s11228-017-0421-z 10.1007/s10589-020-00238-3 10.1007/s11228-011-0191-y 10.1007/s11075-015-0007-5 10.1137/12088255X
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Keywords	Lipschitzian operator 47H10 65K15 65K05 Convex optimization Monotone operator theory Splitting algorithms 90C25 49M29 Cocoercive operator 47H05
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Snippet	In this article, we provide a splitting method for solving monotone inclusions in a real Hilbert space involving four operators: a maximally monotone, a...
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SubjectTerms	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
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Title	Four-Operator Splitting via a Forward–Backward–Half-Forward Algorithm with Line Search
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