General alternative regularization methods for split equality common fixed-point problem

References

• Byrne C. A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Prob. 2004;20:103–120.
   Web of Science ®Google Scholar
• Censor Y, Elfving T. A multiprojection algorithm using Bregman projections in a product space. Numer Algorithms. 1994;8:221–239.
   Google Scholar
• Qu B, Xiu N. A note on the CQ algorithm for the split feasibility problem. Inverse Prob. 2005;21:1655–1665.
   Web of Science ®Google Scholar
• Xu HK. A variable Krasnosel’skiì-Mann algorithm and the multiple-set split feasibility problem. Inverse Prob. 2006;22:2021–2034.
   Web of Science ®Google Scholar
• Yang Q. The relaxed CQ algorithm solving the split feasibility problem. Inverse Prob. 2004;20:1261–1266.
   Web of Science ®Google Scholar
• Yang Q, Zhao J. Generalized KM theorems and their applications. Inverse Prob. 2006;22:833–844.
   Web of Science ®Google Scholar
• Byrne C. Iterative oblique projection onto convex subsets and the split feasibility problem. Inverse Prob. 2002;18:441–453.
   Web of Science ®Google Scholar
• Bauschke HH, Borwein JM. On projection algorithms for solving convex feasibility problems. SIAM Rev. 1996;38(3):367–426.
   Web of Science ®Google Scholar
• Yao Y, Wu J, Liou YC. Regularized methods for the split feasibility problem. Abstract Appl Anal. 2012;2012:13. Article ID 140679.
   Google Scholar
• Xu HK. Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces. Inverse Prob. 2010;26:105018, 17.
   Web of Science ®Google Scholar
• Censor Y, Segal A. The split common fixed point problem for directed operators. J Convex Anal. 2009;16:587–600.
   Web of Science ®Google Scholar
• Censor Y, Chen W, Combettes PL, Davidi R, Herman GT. On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints. Comput Optim Appl. 2012;51:1065–1088.
   Web of Science ®Google Scholar
• Moudafi A. Alternating CQ-algorithm for convex feasibility and split fixed-point problems. J Nonlinear Convex Anal. 2014;15(4):809–818.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• 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.
   PubMed Web of Science ®Google Scholar
• Moudafi A, Al-Shemas E. Simultaneous iterative methods for split equality problems and application. Trans Math Program Appl. 2013;1:1–11.
   Google Scholar
• Halpern B. Fixed points of nonexpanding maps. Bull Am Math Soc. 1967;73:957–961.
   Web of Science ®Google Scholar
• Xu HK. An alternative regularization method for nonexpansive mappings with applications. Contemp Math. 2010;513:239–263.
   Google Scholar
• Moudafi A. Viscosity approximation methods for fixed points problems. J Math Anal Appl. 2000;241(1):46–55.
   Web of Science ®Google Scholar
• Yang C, He S. General alternative regularization methods for nonexpansive mappings in Hilbert spaces. Fixed Point Theory Appl. 2014;2014:203.
   Google Scholar
• Shehu Y. Iterative approximation for split equality fixed point problem for family of multivalued mappings. Revista de la Real Academia de Ciencias Exactas, Físicasy Naturales Serie A Matemáticas. 2015;109(2):627–643.
   Web of Science ®Google Scholar
• Zhao J. Solving split equality fixed-point problem of quasi-nonexpansive mappings without prior knowledge of operators norms. Optim J Math Program Oper Res. 2015;64(12):2619–2630.
   Web of Science ®Google Scholar
• Zhao J, He S. Viscosity approximation methods for split common fixed-point problem of directed operators. Numer Funct Anal Optim. 2015;36(4):528–547.
   Web of Science ®Google Scholar
• López G, Martín-Márquez V, Wang F, Xu HK. Solving the split feasibility problem without prior knowledge of matrix norms. Inverse Prob. 2012;27:085004.
   Web of Science ®Google Scholar
• Zhao J, Yang Q. A simple projection method for solving the multiple-sets split feasibility problem. Inverse Prob Sci Eng. 2013;21(3):537–546.
   Web of Science ®Google Scholar
• Stampacchia G. Formes bilineaires coercivites sur les ensembles convexes. Comptes Rendus de l’Académie des Sciences. 1964;258:4413–4416.
   Google Scholar
• Lions JL, Stampacchia G. Variational inequalities. Commun Pure Appl Math. 1967;20:493–512.
   Web of Science ®Google Scholar
• Goebel K, Kirk WA. Topics in metric fixed point theory, Cambridge studies in advanced mathematics. vol. 28. Cambridge: Cambridge University Press; 1990.
   Google Scholar
• He S, Yang C. Solving the variational inequality problem defined on intersection of finite level sets. Abstract Appl Anal. 2013;2013:19. Article ID 942315.
   Google Scholar
• Tibshirani R. Regression shrinkage and selection via the LASSO. J R Stat Soc Ser B Stat Method. 1996;58:267–288.
   Google Scholar
• Chen S, Donoho D, Saunders M. Atomic decomposition by basis pursuit. SIAM J Sci Comput. 1998;20:33–61.
   Web of Science ®Google Scholar
• Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. CMS books in mathematics. New York (NY): Springer; 2011.
   Google Scholar