References
- Byrne C , Moudafi A . Extensions of the CQ algorithm for the split feasibility and split equality problems. Working paper UAG; 2013.
- Moudafi A . Alternating CQ-algorithm for convex feasibility and split fixed-point problem. J Nonlinear Convex Anal. 2014;15(4):809–818.
- Censor Y , Elfving T . A multiprojection algorithm using Bregman projections in a product space. Numer Algorithms. 1994;8:221–239.
- Attouch H , Cabot H , Frankel F , Peypouquet J . Alternating proximal algorithms for constrained variational inequalities. Application to domain decomposition for PDE’s. Nonlinear Anal. 2011;74(18):7455–7473.
- Attouch H , Bolte J , Redont P , Soubeyran A . Alternating proximal algorithms for weakly coupled minimization problems. Applications to dynamical games and PDEs. J Convex Anal. 2008;15:485–506.
- Censor Y , Bortfeld T , Martin B , Trofimov A . A unified approach for inversion problems in intensity-modulated radiation therapy. Phys Med Biol. 2006;51:2353–2365.
- Attouch H . Alternating minimization and projection algorithms. In: From convexity to nonconvexity, Communication in Instituto Nazionale di Alta Matematica Citta Universitaria -- Roma, Italy; 2009 Jun 8--12.
- Byrne C , Censor Y , Gibali A , Reich S . The split common null point problem. J Nonlinear Convex Anal. 2012;13:759–775.
- Dong QL , He SN . Modified projection algorithms for solving the split equality problems. Sci World J. 2014;328787:7 p.
- Dong QL , He SN . Self-adaptive projection algorithms for solving the split equality problems. Fixed Point Theory. 2017;18(1):191–202.
- Dong QL , Jiang D . Simultaneous and semi-alternating projection algorithms for solving split equality problems. J Inequal Appl. 2018;2018:4.
- Masad E , Reich S . A note on the multiple-set split convex feasibility problem in Hilbert space. J Nonlinear Convex Anal. 2007;8:367–371.
- Moudafi A . A relaxed alternating CQ-algorithm for convex feasibility problems. Nonlinear Anal. 2013;79:117–121.
- Tian D , Shi L , Chen R . Iterative algorithm for solving the multiple-sets split equality problem with split self-adaptive step size in Hilbert spaces. J Inequal Appl. 2016;2016:34.
- Dong QL , He SN , Su F . Strong convergence theorems by shrinking projection methods for class T mappings. Fixed Point Theroy Appl. 2011: 7p. 681214.
- Dong QL , He SN , Zhao J . Solving the split equality problem without prior knowledge of operator norms. Optimization. 2015;64(9):1887–1906.
- Latif A , Eslamian M . Strong convergence of split equality Ky Fan inequality problem. Racsam Rev R Acad A. 2017. DOI:10.1007/s13398-017-0407-6
- Zhao J . Solving split equality fixed-point problem of quasi-nonexpansive mappings without prior knowledge of operators norms. Optimization. 2015;64(12):2619–2630.
- Combettes PL . Strong convergence of block-iterative outer approximation methods for convex optimization. SIAM J Control Optim. 2000;38:538–565.
- Combettes PL . A block-iterative surrogate constraint splitting method for quadratic signal recovery. IEEE Trans Signal Process. 2003;51(7):1771–1782.
- Barlaud M , Belhajali W , Combettes PL , Fillatre L . Classification and regression using an outer approximation projection-gradient method. IEEE Trans Signal Process. 2017;65(17): 4635–4644.
- Dong QL , Gibali A , Jiang D , Ke SH . Convergence of projection and contraction algorithms with outer perturbations and their applications to sparse signals recovery. J Fix Point Theory A. (accepted for publication).
- Dong QL , Gibali A , Jiang D , Tang YC . Bounded perturbation resilience of extragradient-type methods and their applications. J Inequal Appl. (accepted for publication).
- Censor Y , Davidi R , Herman GT . Perturbation resilience and superiorization of iterative algorithms. Inverse Probl. 2010;26:065008 (12 pp.).
- Goebel K , Kirk WA . Topics in metric fixed point theory. Vol. 28, Cambridge studies in advanced mathematics. Cambridge: Cambridge University Press; 1990.
- Pascali P , Sburlan S . Nonlinear mappings of monotone type. Bucharest: Editura Academiei; 1978.
- Tseng P . A modified forward-backward splitting method for maximal monotone mappings. SIAM J Control Optim. 2000;38:431–446.
- Bauschke HH , Combettes PL . Convex analysis and monotone operator theory in Hilbert spaces. 2nd ed. New York (NY): Springer; 2017.
- Fukushima M . A relaxed projection method for variational inequalities. Math Program. 1986;35:58–70.
- Rudin W . Functional analysis. 2nd ed. New York (NY): McGraw-Hill; 1991.
- Hastie T , Rosset S , Tibshirani R , Zhu J . The entire regularization path for the support vector machine. J Mach Learn Res. 2004;5:1391–1415.
- Combettes PL . Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections. IEEE Trans Image Process. 1997;6:493–506.
- Haugazeau Y . Sur les Inéquations Variationnelles et la Minimisation de Fonctionnelles Convexes [Thèse de doctorat]. Université de Paris; 1968.
- Nakajo K , Takahashi W . Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. J Math Anal Appl. 2003;279:372–379.
- Halpern B . Fixed points of nonexpanding maps. Bull Amer Math Soc. 1967;73:957–961.
- Krasnosel’skii MA . Two remarks on the method of successive approximations. Usp Mat Nauk. 1955;10:123–127.
- Mann WR . Mean value methods in iteration. Proc Am Math Soc. 1953;4:506–510.
- Bauschke HH , Combettes PL . A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces. Math Oper Res. 2001;26(2):248–264.
- Khatibzadeh H , Ranjbar S . Halpern type iterations for strongly quasi-nonexpansive sequences and its applications. Taiwan J Math. 2015;19(5):1561–1576.
- He S , Wu T , Cho YJ , Rassias ThM . The optimal parameters selection for a general Halpern iteration. Completed.
- López G , Martín-Márquez V , Wang F , Xu HK . Solving the split feasibility problem without prior knowledge of matrix norms. Inverse Probl. 2012;27:085004.