Superiorization and bounded perturbation resilience of a gradient projection algorithm solving the convex minimization problem

In this article, we use the superiorization methodology to investigate the bounded perturbations resilience of the gradient projection algorithm proposed in Ertürk et al. (J Nonlinear Convex Anal 21(4):943–951, 2020) for solving the convex minimization problem in Hilbert space setting. We obtain tha...

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Vydáno v:	Optimization letters Ročník 17; číslo 8; s. 1957 - 1978
Hlavní autoři:	Ertürk, Müzeyyen, Salkım, Ahmet
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2023
Témata:	Computational Intelligence Mathematics Mathematics and Statistics Numerical and Computational Physics Operations Research/Decision Theory Optimization Original Paper Simulation Gradient projection algorithm Bounded perturbation resilience Convex minimization problems Linear inverse problems Superiorization Split feasibility problems
ISSN:	1862-4472, 1862-4480
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Abstract	In this article, we use the superiorization methodology to investigate the bounded perturbations resilience of the gradient projection algorithm proposed in Ertürk et al. (J Nonlinear Convex Anal 21(4):943–951, 2020) for solving the convex minimization problem in Hilbert space setting. We obtain that the perturbed version of this gradient projection algorithm converges weakly to a solution of the convex minimization problem just like itself. We support our conclusion with an example in an infinitely dimensional Hilbert space. We also show that the superiorization methodology can be applied to the split feasibility and the inverse linear problems with the help of the perturbed gradient projection algorithm.
AbstractList	In this article, we use the superiorization methodology to investigate the bounded perturbations resilience of the gradient projection algorithm proposed in Ertürk et al. (J Nonlinear Convex Anal 21(4):943–951, 2020) for solving the convex minimization problem in Hilbert space setting. We obtain that the perturbed version of this gradient projection algorithm converges weakly to a solution of the convex minimization problem just like itself. We support our conclusion with an example in an infinitely dimensional Hilbert space. We also show that the superiorization methodology can be applied to the split feasibility and the inverse linear problems with the help of the perturbed gradient projection algorithm.
Author	Ertürk, Müzeyyen Salkım, Ahmet
Author_xml	– sequence: 1 givenname: Müzeyyen orcidid: 0000-0002-5328-7995 surname: Ertürk fullname: Ertürk, Müzeyyen email: merturk@adiyaman.edu.tr organization: Department of Mathematics, Adiyaman University – sequence: 2 givenname: Ahmet surname: Salkım fullname: Salkım, Ahmet organization: Department of Mathematics, Adiyaman University
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Cites_doi	10.1090/S0002-9939-1953-0054846-3 10.1090/S0002-9939-1974-0336469-5 10.1109/JSTSP.2007.910263 10.1088/0266-5611/26/6/065008 10.21136/MB.2018.0085-17 10.1006/jmaa.2000.7042 10.1080/00207160.2020.1755430 10.1016/j.cam.2010.12.022 10.1111/j.1475-3995.2009.00695.x 10.1088/1361-6420/33/4/044008 10.4236/ajcm.2012.24048 10.1007/s10957-011-9837-z 10.1088/0266-5611/28/3/035005 10.1007/s10013-020-00463-7 10.1007/BF03007664 10.1007/s10589-015-9777-x 10.1088/0266-5611/26/10/105018 10.1007/s00245-019-09571-4 10.2298/FIL1610829G 10.1007/s10589-012-9491-x 10.1007/s11075-019-00706-w 10.1090/S0002-9904-1967-11761-0 10.1016/0041-5553(66)90114-5 10.1515/auom-2015-0046 10.1017/CBO9780511526152 10.1118/1.4745566
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Copyright	The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Copyright_xml	– notice: The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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References	ErtürkMGursoyFAnsariQHKarakayaVModified picard type iterative algorithm for nonexpansive mappingsJ. Nonlinear Convex Anal.201819691993338301611451.47004 HermanGTGarduñoEDavidiRCensorYSuperiorization: an optimization heuristic for medical physicsMed. Phys.20123995532554610.1118/1.4745566 LevitonESPolyakBTConstrained minimization problemsUSSR Comput. Math. Math. Phys.1966615010.1016/0041-5553(66)90114-5 HermanGSuperiorization for image analysisCombin. Lect. Notes Comput. Sci.201484661732132501486.68232 NikazadTDavidiRHermanGTAccelerated perturbation-resilient block-iterative projection methods with application to image reconstructionInverse Probl.2012283288853010.1088/0266-5611/28/3/0350051261.94014 SahuDRApplications of the S-iteration process to constrained minimization problems and split feasibility problemsFixed Point Theory20111218720427970801281.47053 TakahashiWIntroduction to Nonlinear and Convex Analysis2009YokohamaYokohama Publishers1183.46001 Ansari,Q. H.: Topics in nonlinear analysis and optimization. World Education. Delhi (2012) Censor, Y., Davidi, R., Herman,G.T.: Perturbation resilience and superiorization of iterative algorithms. Inverse Probl. 26(6), 65008 (2010) PhuengrattanaWSuantaiSOn the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary intervalJ. Comput. Appl. Math.201123530063014277128310.1016/j.cam.2010.12.0221215.65095 ErtürkMGursoyFAnsariQHKarakayaVPicard type iterative method with applications to minimization problems and split feasibility problmesJ. Nonlinear Convex Anal.2020214943951410114207347531 Ertürk, M., Kızmaz, A.: A new gradient projection algorithm for convex minimization problem and its application to split feasibility problem. Vietnam J. Math. 50, 1–16 (2021) Censor,Y.: Weak and strong superiorization: between feasibility-seeking and minimization. Analele Universitatii" Ovidius" Constanta-Seria Matematica, 23(3), 41–54 (2015) MannWRMean value methods in iterationProc. Am. Math. Soc.1953435065105484610.1090/S0002-9939-1953-0054846-30050.11603 IshikawaSFixed points by a new iteration methodProc. Am. Math. Soc.197444114715033646910.1090/S0002-9939-1974-0336469-50286.47036 DavidiaRHermanaGCensorYPerturbation-resilient block-iterative projection methods with application to image reconstruction from projectionsInt. Trans. Oper. Res.200916505524253825310.1111/j.1475-3995.2009.00695.x AgarwalRPO’ReganDSahuDRFixed Point Theory for Lipschitzian-Type Mappings with Applications2009New YorkSpringer1176.47037 ButnariuDDavidiRHermanGTKazantsevIGStable convergence behavior under summable perturbations of a class of projection methods for convex feasibility and optimization problemsIEEE J. Sel. Top. Signal Process.2007154054710.1109/JSTSP.2007.910263 Gürsoy, F.: A Picard-S iterative method for approximating fixed point of weak contraction mappings. Filomat 30(10), 2829–2845 (2016) OpialZWeak convergence of the sequence of successive approximations for nonexpansive mappingsBull. Am. Math. Soc.196773459159721130110.1090/S0002-9904-1967-11761-00179.19902 GürsoyFErtürkMAbbasMA Picard-type iterative algorithm for general variational inequalities and nonexpansive mappingsNumer. Algorithms2020833867883406435610.1007/s11075-019-00706-w1513.47120 BonackerEGibaliAKüferKHAccelerating two projection methods via perturbations with application to intensity-modulated radiation therapyAppl. Math. Optim.2021832881914423980310.1007/s00245-019-09571-41468.65069 Gürsoy, F., Karakaya, V.: A Picard-S hybrid type iteration method for solving a differential equation with retarted argument. arXiv:1403.2546 (2014) JinWCensorYJiangMBounded perturbation resilience of projected scaled gradient methodsComput. Optim. Appl.2016632365392345744510.1007/s10589-015-9777-x1339.90262 CensorYZaslavskiAJConvergence and perturbation resilience of dynamic string-averaging projection methodsComput. Optim. Appl.2013546576300341710.1007/s10589-012-9491-x1285.90079 ErtürkMGürsoyFŞimşekNS-iterative algorithm for solving variational inequalitiesInt. J. Comput. Math.2021983435448422761110.1080/00207160.2020.17554301483.49014 NoorMANew approximation schemes for general variational inequalitiesJ. Math. Anal. Appl.2000251217229179040610.1006/jmaa.2000.70420964.49007 AgarwalRPReganDOSahuDRIterative construction of fixed points of nearly asymptotically nonexpansive mappingsJ. Nonlinear Convex Anal.20078617923146661134.47047 Picard, E.: Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives. Journal de Mathématiques pures et appliquées 6, 145–210 (1890) BaillonJBHaddadGQuelques proprietes des operateurs angle-bornes et n-cycliquement monotonesIsr. J. Math.19772613715050027910.1007/BF030076640352.47023 Xu, H.K.: Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces. Inverse Probl. 26, 105018 (2010) ErtürkMGürsoyFSome convergence, stability and data dependency results for a Picard-S iteration method of quasi-strictly contractive operatorsMath. Bohem.201914416983393419810.21136/MB.2018.0085-171474.47144 Goebel, K., Kirk, W.A.: Topics in Metric Fixed Point Theory. Cambridge University Press, vol. 28 (1990) Xu, H.K.: Bounded perturbation resilience and superiorization techniques for the projected scaled gradient method. Inverse Probl. 33(4) (2017) ChughRKumarVKumarSStrong Convergence of a new three step iterative scheme in Banach spacesAm. J. Comput. Math.2012234535710.4236/ajcm.2012.24048 Polyak, B.T.: Introduction to optimization, ser. Translations series in mathematics and engineering, Optimization Software. Optimization Software Inc. Publications, New York (1987) XuHKAveraged mappings and the gradient-projection algorithmJ. Optim. Theory Appl.20111502360378281892610.1007/s10957-011-9837-z1233.90280 RP Agarwal (1961_CR2) 2007; 8 D Butnariu (1961_CR6) 2007; 1 M Ertürk (1961_CR14) 2020; 21 G Herman (1961_CR22) 2014; 8466 GT Herman (1961_CR21) 2012; 39 F Gürsoy (1961_CR17) 2020; 83 M Ertürk (1961_CR12) 2019; 144 1961_CR20 S Ishikawa (1961_CR23) 1974; 44 W Phuengrattana (1961_CR31) 2011; 235 W Takahashi (1961_CR34) 2009 RP Agarwal (1961_CR1) 2009 HK Xu (1961_CR36) 2011; 150 E Bonacker (1961_CR5) 2021; 83 MA Noor (1961_CR28) 2000; 251 M Ertürk (1961_CR13) 2018; 19 WR Mann (1961_CR26) 1953; 4 DR Sahu (1961_CR33) 2011; 12 1961_CR3 1961_CR35 Y Censor (1961_CR8) 2013; 54 R Chugh (1961_CR10) 2012; 2 1961_CR37 1961_CR30 JB Baillon (1961_CR4) 1977; 26 1961_CR7 1961_CR32 1961_CR9 M Ertürk (1961_CR15) 2021; 98 Z Opial (1961_CR29) 1967; 73 R Davidia (1961_CR11) 2009; 16 1961_CR16 1961_CR18 1961_CR19 ES Leviton (1961_CR25) 1966; 6 T Nikazad (1961_CR27) 2012; 28 W Jin (1961_CR24) 2016; 63
References_xml	– reference: ChughRKumarVKumarSStrong Convergence of a new three step iterative scheme in Banach spacesAm. J. Comput. Math.2012234535710.4236/ajcm.2012.24048 – reference: SahuDRApplications of the S-iteration process to constrained minimization problems and split feasibility problemsFixed Point Theory20111218720427970801281.47053 – reference: BaillonJBHaddadGQuelques proprietes des operateurs angle-bornes et n-cycliquement monotonesIsr. J. Math.19772613715050027910.1007/BF030076640352.47023 – reference: BonackerEGibaliAKüferKHAccelerating two projection methods via perturbations with application to intensity-modulated radiation therapyAppl. Math. Optim.2021832881914423980310.1007/s00245-019-09571-41468.65069 – reference: Polyak, B.T.: Introduction to optimization, ser. Translations series in mathematics and engineering, Optimization Software. Optimization Software Inc. Publications, New York (1987) – reference: HermanGTGarduñoEDavidiRCensorYSuperiorization: an optimization heuristic for medical physicsMed. Phys.20123995532554610.1118/1.4745566 – reference: JinWCensorYJiangMBounded perturbation resilience of projected scaled gradient methodsComput. Optim. Appl.2016632365392345744510.1007/s10589-015-9777-x1339.90262 – reference: CensorYZaslavskiAJConvergence and perturbation resilience of dynamic string-averaging projection methodsComput. Optim. Appl.2013546576300341710.1007/s10589-012-9491-x1285.90079 – reference: Xu, H.K.: Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces. Inverse Probl. 26, 105018 (2010) – reference: LevitonESPolyakBTConstrained minimization problemsUSSR Comput. Math. Math. Phys.1966615010.1016/0041-5553(66)90114-5 – reference: OpialZWeak convergence of the sequence of successive approximations for nonexpansive mappingsBull. Am. Math. Soc.196773459159721130110.1090/S0002-9904-1967-11761-00179.19902 – reference: ErtürkMGürsoyFŞimşekNS-iterative algorithm for solving variational inequalitiesInt. J. Comput. Math.2021983435448422761110.1080/00207160.2020.17554301483.49014 – reference: MannWRMean value methods in iterationProc. Am. Math. Soc.1953435065105484610.1090/S0002-9939-1953-0054846-30050.11603 – reference: Picard, E.: Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives. Journal de Mathématiques pures et appliquées 6, 145–210 (1890) – reference: Goebel, K., Kirk, W.A.: Topics in Metric Fixed Point Theory. Cambridge University Press, vol. 28 (1990) – reference: NikazadTDavidiRHermanGTAccelerated perturbation-resilient block-iterative projection methods with application to image reconstructionInverse Probl.2012283288853010.1088/0266-5611/28/3/0350051261.94014 – reference: AgarwalRPO’ReganDSahuDRFixed Point Theory for Lipschitzian-Type Mappings with Applications2009New YorkSpringer1176.47037 – reference: ErtürkMGürsoyFSome convergence, stability and data dependency results for a Picard-S iteration method of quasi-strictly contractive operatorsMath. Bohem.201914416983393419810.21136/MB.2018.0085-171474.47144 – reference: ErtürkMGursoyFAnsariQHKarakayaVPicard type iterative method with applications to minimization problems and split feasibility problmesJ. Nonlinear Convex Anal.2020214943951410114207347531 – reference: ErtürkMGursoyFAnsariQHKarakayaVModified picard type iterative algorithm for nonexpansive mappingsJ. Nonlinear Convex Anal.201819691993338301611451.47004 – reference: DavidiaRHermanaGCensorYPerturbation-resilient block-iterative projection methods with application to image reconstruction from projectionsInt. Trans. Oper. Res.200916505524253825310.1111/j.1475-3995.2009.00695.x – reference: PhuengrattanaWSuantaiSOn the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary intervalJ. Comput. Appl. Math.201123530063014277128310.1016/j.cam.2010.12.0221215.65095 – reference: Ertürk, M., Kızmaz, A.: A new gradient projection algorithm for convex minimization problem and its application to split feasibility problem. Vietnam J. Math. 50, 1–16 (2021) – reference: TakahashiWIntroduction to Nonlinear and Convex Analysis2009YokohamaYokohama Publishers1183.46001 – reference: Gürsoy, F., Karakaya, V.: A Picard-S hybrid type iteration method for solving a differential equation with retarted argument. arXiv:1403.2546 (2014) – reference: Gürsoy, F.: A Picard-S iterative method for approximating fixed point of weak contraction mappings. Filomat 30(10), 2829–2845 (2016) – reference: NoorMANew approximation schemes for general variational inequalitiesJ. Math. Anal. Appl.2000251217229179040610.1006/jmaa.2000.70420964.49007 – reference: Xu, H.K.: Bounded perturbation resilience and superiorization techniques for the projected scaled gradient method. Inverse Probl. 33(4) (2017) – reference: IshikawaSFixed points by a new iteration methodProc. Am. Math. Soc.197444114715033646910.1090/S0002-9939-1974-0336469-50286.47036 – reference: HermanGSuperiorization for image analysisCombin. Lect. Notes Comput. Sci.201484661732132501486.68232 – reference: Ansari,Q. H.: Topics in nonlinear analysis and optimization. World Education. Delhi (2012) – reference: Censor, Y., Davidi, R., Herman,G.T.: Perturbation resilience and superiorization of iterative algorithms. Inverse Probl. 26(6), 65008 (2010) – reference: XuHKAveraged mappings and the gradient-projection algorithmJ. Optim. Theory Appl.20111502360378281892610.1007/s10957-011-9837-z1233.90280 – reference: ButnariuDDavidiRHermanGTKazantsevIGStable convergence behavior under summable perturbations of a class of projection methods for convex feasibility and optimization problemsIEEE J. Sel. Top. Signal Process.2007154054710.1109/JSTSP.2007.910263 – reference: Censor,Y.: Weak and strong superiorization: between feasibility-seeking and minimization. Analele Universitatii" Ovidius" Constanta-Seria Matematica, 23(3), 41–54 (2015) – reference: GürsoyFErtürkMAbbasMA Picard-type iterative algorithm for general variational inequalities and nonexpansive mappingsNumer. Algorithms2020833867883406435610.1007/s11075-019-00706-w1513.47120 – reference: AgarwalRPReganDOSahuDRIterative construction of fixed points of nearly asymptotically nonexpansive mappingsJ. Nonlinear Convex Anal.20078617923146661134.47047 – volume: 4 start-page: 506 issue: 3 year: 1953 ident: 1961_CR26 publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-1953-0054846-3 – volume: 44 start-page: 147 issue: 1 year: 1974 ident: 1961_CR23 publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-1974-0336469-5 – volume-title: Introduction to Nonlinear and Convex Analysis year: 2009 ident: 1961_CR34 – volume: 1 start-page: 540 year: 2007 ident: 1961_CR6 publication-title: IEEE J. Sel. Top. Signal Process. doi: 10.1109/JSTSP.2007.910263 – ident: 1961_CR7 doi: 10.1088/0266-5611/26/6/065008 – volume: 144 start-page: 69 issue: 1 year: 2019 ident: 1961_CR12 publication-title: Math. Bohem. doi: 10.21136/MB.2018.0085-17 – volume: 251 start-page: 217 year: 2000 ident: 1961_CR28 publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.2000.7042 – volume: 8 start-page: 61 year: 2007 ident: 1961_CR2 publication-title: J. Nonlinear Convex Anal. – volume: 98 start-page: 435 issue: 3 year: 2021 ident: 1961_CR15 publication-title: Int. J. Comput. Math. doi: 10.1080/00207160.2020.1755430 – volume: 235 start-page: 3006 year: 2011 ident: 1961_CR31 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2010.12.022 – volume: 21 start-page: 943 issue: 4 year: 2020 ident: 1961_CR14 publication-title: J. Nonlinear Convex Anal. – volume: 16 start-page: 505 year: 2009 ident: 1961_CR11 publication-title: Int. Trans. Oper. Res. doi: 10.1111/j.1475-3995.2009.00695.x – ident: 1961_CR37 doi: 10.1088/1361-6420/33/4/044008 – volume: 2 start-page: 345 year: 2012 ident: 1961_CR10 publication-title: Am. J. Comput. Math. doi: 10.4236/ajcm.2012.24048 – volume: 19 start-page: 919 issue: 6 year: 2018 ident: 1961_CR13 publication-title: J. Nonlinear Convex Anal. – volume: 150 start-page: 360 issue: 2 year: 2011 ident: 1961_CR36 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-011-9837-z – ident: 1961_CR30 – volume: 28 issue: 3 year: 2012 ident: 1961_CR27 publication-title: Inverse Probl. doi: 10.1088/0266-5611/28/3/035005 – ident: 1961_CR16 doi: 10.1007/s10013-020-00463-7 – ident: 1961_CR32 – volume: 26 start-page: 137 year: 1977 ident: 1961_CR4 publication-title: Isr. J. Math. doi: 10.1007/BF03007664 – volume: 63 start-page: 365 issue: 2 year: 2016 ident: 1961_CR24 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-015-9777-x – ident: 1961_CR35 doi: 10.1088/0266-5611/26/10/105018 – volume: 12 start-page: 187 year: 2011 ident: 1961_CR33 publication-title: Fixed Point Theory – volume: 83 start-page: 881 issue: 2 year: 2021 ident: 1961_CR5 publication-title: Appl. Math. Optim. doi: 10.1007/s00245-019-09571-4 – ident: 1961_CR18 doi: 10.2298/FIL1610829G – volume: 54 start-page: 65 year: 2013 ident: 1961_CR8 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-012-9491-x – volume: 83 start-page: 867 issue: 3 year: 2020 ident: 1961_CR17 publication-title: Numer. Algorithms doi: 10.1007/s11075-019-00706-w – volume: 73 start-page: 591 issue: 4 year: 1967 ident: 1961_CR29 publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0002-9904-1967-11761-0 – ident: 1961_CR3 – ident: 1961_CR19 – volume: 6 start-page: 1 year: 1966 ident: 1961_CR25 publication-title: USSR Comput. Math. Math. Phys. doi: 10.1016/0041-5553(66)90114-5 – ident: 1961_CR9 doi: 10.1515/auom-2015-0046 – volume-title: Fixed Point Theory for Lipschitzian-Type Mappings with Applications year: 2009 ident: 1961_CR1 – volume: 8466 start-page: 1 year: 2014 ident: 1961_CR22 publication-title: Combin. Lect. Notes Comput. Sci. – ident: 1961_CR20 doi: 10.1017/CBO9780511526152 – volume: 39 start-page: 5532 issue: 9 year: 2012 ident: 1961_CR21 publication-title: Med. Phys. doi: 10.1118/1.4745566
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Snippet	In this article, we use the superiorization methodology to investigate the bounded perturbations resilience of the gradient projection algorithm proposed in...
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Title	Superiorization and bounded perturbation resilience of a gradient projection algorithm solving the convex minimization problem
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