Two new self-adaptive algorithms for solving the split common null point problem with multiple output sets in Hilbert spaces
To solve the split common null point problem with multiple output sets in Hilbert spaces, we introduce two new self-adaptive algorithms and prove strong convergence theorems for both of them.
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| Vydané v: | Fixed point theory and algorithms for sciences and engineering Ročník 23; číslo 2; s. 16 |
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| Jazyk: | English |
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01.05.2021
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| Abstract | To solve the split common null point problem with multiple output sets in Hilbert spaces, we introduce two new self-adaptive algorithms and prove strong convergence theorems for both of them. |
|---|---|
| AbstractList | To solve the split common null point problem with multiple output sets in Hilbert spaces, we introduce two new self-adaptive algorithms and prove strong convergence theorems for both of them. |
| ArticleNumber | 16 |
| Author | Tuyen, Truong Minh Reich, Simeon |
| Author_xml | – sequence: 1 givenname: Simeon surname: Reich fullname: Reich, Simeon organization: Department of Mathematics, The Technion, Israel Institute of Technology – sequence: 2 givenname: Truong Minh surname: Tuyen fullname: Tuyen, Truong Minh email: tuyentm@tnus.edu.vn organization: Department of Mathematics and Informatics, Thai Nguyen University of Sciences |
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| Keywords | split common null point problem 47H10 metric projection 49J53 90C25 self-adaptive algorithm 47H09 nonexpansive mapping Hilbert space |
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| References | ReichSTuyenTMA new algorithm for solving the split common null point problem in Hilbert spacesNumer. Algorithms202083789805405526907160103 ButnariuDResmeritaEBregman distances, totally convex functions and a method for solving operator equations in Banach spacesAbstr. Appl. Anal.2006200613922116751130.47046 ByrneCA unified treatment of some iterative algorithms in signal processing and image reconstructionInverse Probl.20042010312020446081051.65067 MaingéPEA viscosity method with no spectral radius requirements for the split common fixed point problemEJOR20142351172731598971305.65146 YangQThe relaxed CQ algorithm for solving the split feasibility problemInverse Probl.2004201261126620879891066.65047 TakahashiSTakahashiWToyodaMStrong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spacesJ. Optim. Theory Appl.2010147274127205901208.47071 DadashiVShrinking projection algorithms for the split common null point problemBull. Aust. Math. Soc.201799299306370391106792046 TakahashiWThe split common null point problem in Banach spacesArch. Math.201510435736533257701458.47034 ReichSTuyenTMThe split feasibility problem with multiple output sets in Hilbert spacesOptim. Lett.20201423352353416361607311820 AgarwalRPO’ReganDSahuDRFixed Point Theory for Lipschitzian-type Mappings with Applications2009New YorkSpringer1176.47037 IidukaHProximal point algorithms for nonsmooth convex optimization with fixed point constraintsEJOR2015253250351334851881346.90663 ByrneCIterative oblique projection onto convex sets and the split feasibility problemInverse Probl.20021844145319102480996.65048 XuH-KIterative methods for the split feasibility problem in infinite dimensional Hilbert spacesInverse Probl.20102610501827197791213.65085 CensorYGibaliAReichSAlgorithms for the split variational inequality problemsNumer. Algorithms20125930132328731361239.65041 GoebelKKirkWATopics in Metric Fixed Point Theory, Cambridge Stud. Adv. Math.1990CambridgeCambridge University Press BauschkeHHMatouškováEReichSProjection and proximal point methods: Convergence results and counterexamplesNonlinear Anal.20045671573820367871059.47060 ByrneCCensorYGibaliAReichSThe split common null point problemJ. Nonlinear Convex Anal.20121375977530151191262.47073 TakahashiWThe split feasibility problem and the shrinking projection method in Banach spacesJ. Nonlinear Convex Anal.2015161449145933759771343.47074 TuyenTMHaNSA strong convergence theorem for solving the split feasibility and fixed point problems in Banach spacesJ. Fixed Point Theory Appl.20182014038562701398.65130 GoebelKReichSUniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings1984New YorkMarcel Dekker0537.46001 ReichSTuyenTMIterative methods for solving the generalized split common null point problem in Hilbert spacesOptimization2020691013103840955721445.47043 GülerOOn the convergence of the proximal point algorithm for convex minimizationSIAM J. Control Optim.19912940341910927350737.90047 RockafellarRTOn the maximal monotonicity of subdifferential mappingsPac. J. Math.1970332092162628270199.47101 CensorYSegalAThe split common fixed point problem for directed operatorsJ. Convex Anal.20091658760025599611189.65111 WangFXuH-KCyclic algorithms for split feasibility problems in Hilbert spacesNonlinear Anal.2011744105411128029901308.47079 TakahashiSTakahashiWThe split common null point problem and the shrinking projection method in Banach spacesOptimization20166528128734381101338.47110 MaingéPEStrong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimizationSet-Valued Anal.20081689991224660271156.90426 XuH-KA variable Krasnosel’skii–Mann algorithm and the multiple-set split feasibility problemInverse Probl.200622202120341126.47057 TuyenTMThuyNTTTrangNMA strong convergence theorem for a parallel iterative method for solving the split common null point problem in Hilbert spacesJ. Optim. Theory Appl.20191382271291398930707112086 XuH-KA regularization method for the proximal point algorithmJ. Glob. Optim.20063611512522568861131.90062 MasadEReichSA note on the multiple-set split convex feasibility problem in Hilbert spaceJ. Nonlinear Convex Anal.2007836737123778591171.90009 ReichSTuyenTMTrangNMParallel iterative methods for solving the split common fixed point problem in Hilbert spacesNumer. Funct. Anal. Optim.20204177880540805291442.47064 CensorYElfvingTA multi projection algorithm using Bregman projections in a product spaceNumer. Algorithms1994822123913092220828.65065 ReichSTuyenTMTwo projection methods for solving the multiple-set split common null point problem in Hilbert spacesOptimization202069919131934413906207249879 RockafellarRTMonotone operators and the proximal point algorithmSIAM J. Control Optim.1976148778984104830358.90053 LandweberLAn iterative formula for Fredholm integral equations of the first kindAm. J. Math.195173615624433480043.10602 XuH-KStrong convergence of an iterative method for nonexpansive and accretive operatorsJ. Math. Anal. Appl.200631463164321852551086.47060 TuyenTMHaNSThuyNTTA shrinking projection method for solving the split common null point problem in Banach spacesNumer. Algorithms201981813832396137907072079 CensorYElfvingTKopfNBortfeldTThe multiple-sets split feasibility problem and its applicationInverse Probl.2005212071208421836681089.65046 LehdiliNMoudafiACombining the proximal algorithm and Tikhonov regularizationOptimization19963723925213962380863.49018 MoudafiAThe split common fixed point problem for demicontractive mappingsInverse Probl.20102605500726471491219.90185 TuyenTMA strong convergence theorem for the split common null point problem in Banach spacesAppl. Math. Optim.201979207227390378507043109 H-K Xu (848_CR40) 2006; 22 H Iiduka (848_CR15) 2015; 253 D Butnariu (848_CR3) 2006; 2006 PE Maingé (848_CR18) 2008; 16 S Reich (848_CR23) 2020; 14 O Güler (848_CR14) 1991; 29 S Takahashi (848_CR29) 2016; 65 RT Rockafellar (848_CR27) 1970; 33 Y Censor (848_CR10) 2012; 59 K Goebel (848_CR12) 1990 K Goebel (848_CR13) 1984 C Byrne (848_CR5) 2004; 20 E Masad (848_CR20) 2007; 8 Y Censor (848_CR8) 2009; 16 C Byrne (848_CR6) 2012; 13 TM Tuyen (848_CR36) 2018; 20 TM Tuyen (848_CR33) 2019; 138 H-K Xu (848_CR38) 2006; 36 A Moudafi (848_CR21) 2010; 26 PE Maingé (848_CR19) 2014; 235 F Wang (848_CR37) 2011; 74 Q Yang (848_CR42) 2004; 20 Y Censor (848_CR9) 2005; 21 H-K Xu (848_CR39) 2006; 314 HH Bauschke (848_CR2) 2004; 56 RT Rockafellar (848_CR28) 1976; 14 V Dadashi (848_CR11) 2017; 99 S Reich (848_CR25) 2020; 69 S Takahashi (848_CR30) 2010; 147 Y Censor (848_CR7) 1994; 8 N Lehdili (848_CR17) 1996; 37 W Takahashi (848_CR31) 2015; 16 S Reich (848_CR26) 2020; 83 W Takahashi (848_CR32) 2015; 104 L Landweber (848_CR16) 1951; 73 TM Tuyen (848_CR34) 2019; 79 S Reich (848_CR24) 2020; 41 H-K Xu (848_CR41) 2010; 26 C Byrne (848_CR4) 2002; 18 RP Agarwal (848_CR1) 2009 S Reich (848_CR22) 2020; 69 TM Tuyen (848_CR35) 2019; 81 |
| References_xml | – reference: CensorYElfvingTKopfNBortfeldTThe multiple-sets split feasibility problem and its applicationInverse Probl.2005212071208421836681089.65046 – reference: MaingéPEStrong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimizationSet-Valued Anal.20081689991224660271156.90426 – reference: MaingéPEA viscosity method with no spectral radius requirements for the split common fixed point problemEJOR20142351172731598971305.65146 – reference: RockafellarRTOn the maximal monotonicity of subdifferential mappingsPac. J. Math.1970332092162628270199.47101 – reference: TakahashiSTakahashiWThe split common null point problem and the shrinking projection method in Banach spacesOptimization20166528128734381101338.47110 – reference: ReichSTuyenTMIterative methods for solving the generalized split common null point problem in Hilbert spacesOptimization2020691013103840955721445.47043 – reference: ReichSTuyenTMThe split feasibility problem with multiple output sets in Hilbert spacesOptim. Lett.20201423352353416361607311820 – reference: XuH-KA variable Krasnosel’skii–Mann algorithm and the multiple-set split feasibility problemInverse Probl.200622202120341126.47057 – reference: TuyenTMHaNSThuyNTTA shrinking projection method for solving the split common null point problem in Banach spacesNumer. Algorithms201981813832396137907072079 – reference: LandweberLAn iterative formula for Fredholm integral equations of the first kindAm. J. Math.195173615624433480043.10602 – reference: GoebelKReichSUniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings1984New YorkMarcel Dekker0537.46001 – reference: ReichSTuyenTMA new algorithm for solving the split common null point problem in Hilbert spacesNumer. Algorithms202083789805405526907160103 – reference: DadashiVShrinking projection algorithms for the split common null point problemBull. Aust. Math. Soc.201799299306370391106792046 – reference: CensorYElfvingTA multi projection algorithm using Bregman projections in a product spaceNumer. Algorithms1994822123913092220828.65065 – reference: TakahashiWThe split common null point problem in Banach spacesArch. Math.201510435736533257701458.47034 – reference: MoudafiAThe split common fixed point problem for demicontractive mappingsInverse Probl.20102605500726471491219.90185 – reference: BauschkeHHMatouškováEReichSProjection and proximal point methods: Convergence results and counterexamplesNonlinear Anal.20045671573820367871059.47060 – reference: WangFXuH-KCyclic algorithms for split feasibility problems in Hilbert spacesNonlinear Anal.2011744105411128029901308.47079 – reference: ByrneCCensorYGibaliAReichSThe split common null point problemJ. Nonlinear Convex Anal.20121375977530151191262.47073 – reference: ByrneCIterative oblique projection onto convex sets and the split feasibility problemInverse Probl.20021844145319102480996.65048 – reference: MasadEReichSA note on the multiple-set split convex feasibility problem in Hilbert spaceJ. Nonlinear Convex Anal.2007836737123778591171.90009 – reference: ReichSTuyenTMTrangNMParallel iterative methods for solving the split common fixed point problem in Hilbert spacesNumer. Funct. Anal. Optim.20204177880540805291442.47064 – reference: TuyenTMThuyNTTTrangNMA strong convergence theorem for a parallel iterative method for solving the split common null point problem in Hilbert spacesJ. Optim. Theory Appl.20191382271291398930707112086 – reference: AgarwalRPO’ReganDSahuDRFixed Point Theory for Lipschitzian-type Mappings with Applications2009New YorkSpringer1176.47037 – reference: ReichSTuyenTMTwo projection methods for solving the multiple-set split common null point problem in Hilbert spacesOptimization202069919131934413906207249879 – reference: RockafellarRTMonotone operators and the proximal point algorithmSIAM J. Control Optim.1976148778984104830358.90053 – reference: CensorYGibaliAReichSAlgorithms for the split variational inequality problemsNumer. 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| SubjectTerms | Adaptive algorithms Algorithms Analysis Feasibility Hilbert space Iterative methods Mathematical Methods in Physics Mathematics Mathematics and Statistics Regularization methods Theorems |
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| Title | Two new self-adaptive algorithms for solving the split common null point problem with multiple output sets in Hilbert spaces |
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