Convergence rates of the modified forward reflected backward splitting algorithm in Banach spaces

Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth in Banach space. In this paper, we introduce a non-traditional forward-backward splitting method for solving such minimization problem. We establish different convergence estimates under dif...

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Veröffentlicht in:AIMS mathematics Jg. 8; H. 5; S. 12195 - 12216
Hauptverfasser: Guan, Weibo, Song, Wen
Format: Journal Article
Sprache:Englisch
Veröffentlicht: AIMS Press 01.01.2023
Schlagworte:
banach spaces
convergence rate
forward-backward splitting algorithm
ISSN:2473-6988, 2473-6988
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Abstract Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth in Banach space. In this paper, we introduce a non-traditional forward-backward splitting method for solving such minimization problem. We establish different convergence estimates under different stepsize assumptions.
AbstractList Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth in Banach space. In this paper, we introduce a non-traditional forward-backward splitting method for solving such minimization problem. We establish different convergence estimates under different stepsize assumptions.
Author Song, Wen
Guan, Weibo
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Cites_doi 10.1007/s11228-010-0147-7
10.1080/01630563.2015.1037591
10.48550/arXiv.funct-an/9311001
10.1137/16M105592X
10.1109/78.330356
10.1088/0266-5611/25/1/015005
10.1007/BF00282247
10.1002/cmm4.1088
10.1007/s11590-011-0286-2
10.1155/S1085337597000298
10.1007/1-4020-4396-1
10.1137/18M1207260
10.2140/PJM.1972.40.565
10.1137/0716071
10.1137/110820300
10.1137/S105262340139611X
10.1016/j.na.2010.04.077
10.1007/978-94-009-2121-4
10.1007/s11590-020-01544-9
10.1137/050626090
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Snippet Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth in Banach space. In this paper, we introduce a...
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SubjectTerms banach spaces
convergence rate
forward-backward splitting algorithm
Title Convergence rates of the modified forward reflected backward splitting algorithm in Banach spaces
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