Inertial accelerated algorithms for the split common fixed-point problem of directed operators

References

• 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, Elfving T. A multiprojection algorithm using Bregman projections in a product space. Numer Algor. 1994;8:221–239.
   Google Scholar
• Byrne C. A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Probl. 2004;20:103–120.
   Web of Science ®Google Scholar
• Byrne C. Iterative oblique projection onto convex subsets and the split feasibility problem. Inverse Probl. 2002;18:441–453.
   Web of Science ®Google Scholar
• Censor Y, Bortfeld T, Martin B, et al. A unified approach for inversion problems in intensity modulated radiation therapy. Phys Med Biol. 2006;51:2353–2365.
   PubMed Web of Science ®Google Scholar
• Combettes PL. The convex feasibility problem in image recovery. Adv Imaging Electron Phys. 1996;95:155–270.
   Google Scholar
• Bauschke HH, Borwein JM. On projection algorithms for solving convex feasibility problems. SIAM Rev. 1996;38:367–426.
   Web of Science ®Google Scholar
• Chang SS, Kim JK, Cho YJ, et al. Weak and strong convergence theorems of solutions to split feasibility problem for nonspreading type mapping in Hilbert spaces. Fixed Point Theory Appl. 2014;2014:11.
   Google Scholar
• Qin X, Wang L. A fixed point method for solving a split feasibility problem in Hilbert spaces. RACSAM. 2019;113:315–325.
   Google Scholar
• Qin X, Petrusel A, Yao JC. CQ iterative algorithms for fixed points of nonexpansive mappings and split feasibility problems in Hilbert spaces. J Nonlinear Convex Anal. 2018;19:157–165.
   Web of Science ®Google Scholar
• Xu HK. A variable Krasnosel'ski i˘-Mann algorithm and the multiple-set split feasibility problem. Inverse Probl. 2006;22:2021–2034.
   Web of Science ®Google Scholar
• Xu HK. Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces. Inverse Probl. 2010;26:105018. 17pages.
   Web of Science ®Google Scholar
• Yao Y, Yao Z, Abdou AA, et al. Self-adaptive algorithms for proximal split feasibility problems and strong convergence analysis. Fixed Point Theory Appl. 2015;2015:1168.
   Google Scholar
• Qu B, Xiu N. A note on the CQ algorithm for the split feasibility problem. Inverse Probl. 2005;21:1655–1665.
   Web of Science ®Google Scholar
• Wang F. A new method for split common fixed-point problem without priori knowledge of operator norms. J Fixed Point Theory Appl. 2017;19:2427–2436.
   Web of Science ®Google Scholar
• Yang Q. On variable-step relaxed projection algorithm for variational inequalities. J Math Anal Appl. 2005;302:166–179.
   Web of Science ®Google Scholar
• Zhou H, Wang P. Adaptively relaxed algorithms for solving the split feasibility problem with a new step size. J Inequal Appl. 2014;2014:221.
   Google Scholar
• Lopez G, Martin V, Wang F, et al. Solving the split feasibility problem without prior knowledge of matrix norms. Inverse Probl. 2012;28:085004.
   Web of Science ®Google Scholar
• Chen P, Huang J, Zhang X. A primal-dual fixed point algorithm for convex separable minimization with applications to image restoration. Inverse Probl. 2013;29:025011. (33pp).
   Web of Science ®Google Scholar
• Zhao J, Hou D. A self-adaptive iterative algorithm for the split common fixed point problems. Numer Algor. 2019;82:1047–1063.
   Web of Science ®Google Scholar
• Cegielski A. General method for solving the split common fixed point problem. J Optim Theory Appl. 2015;165:385–404.
   Web of Science ®Google Scholar
• Eslamian M, Eskandani GZ, Raeisi M. Split common null point and common fixed point problems between Banach spaces and Hilbert spaces. Mediterr J Math. 2017;14:119. 15 pages.
   Web of Science ®Google Scholar
• Giang DM, Strodiot JJ, Nguyen VH. Strong convergence of an iterative method for solving the multiple-set split equality fixed point problem in a real Hilbert space. RACSAM. 2017;111:983–998.
   Google Scholar
• Moudafi A. A note on the split common fixed point problem for quasi-nonexpansive operators. Nonlinear Anal. 2011;74:4083–4087.
   Web of Science ®Google Scholar
• Yang L, Zhao F, Kim JK. The split common fixed point problem for demicontractive mappings in Banach spaces. J Computational Anal Appl. 2017;22(5):858–863.
   Google Scholar
• Zhao J, He S. Viscosity approximation methods for split common fixed-point problem of directed operators. Numer Funct Anal Optim. 2015;36:528–547.
   Web of Science ®Google Scholar
• Polyak BT. Some methods of speeding up the convergence of iteration methods. USSR Comput Math Math Phys. 1964;4:1–17.
   Google Scholar
• Nesterov Y. A method for solving the convex programming problem with convergence rate O(1/k2). Dokl Akad Nauk SSSR. 1983;269:543–547.
   Web of Science ®Google Scholar
• Alvarez F, Attouch H. An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set Valued Anal. 2001;9:3–11.
   Web of Science ®Google Scholar
• Maingé PE. Convergence theorems for inertial KM-type algorithms. J Comput Appl Math. 2008;219:223–236.
   Web of Science ®Google Scholar
• Dang Y, Sun J, Xu H. Inertial accelerated algorithms for solving a split feasibility problem. J Indus Manage Optim. 2017;13:1383–1394.
   Web of Science ®Google Scholar
• Gibali A, Mai DT, Vinh NT. A new relaxed CQ algorithm for solving split feasibility problems in Hilbert spaces and its applications. J Indus Manage Optim. 2019;15(2):963–984.
   Google Scholar
• Shehu Y, Vuong PT, Cholamjiak P. A self-adaptive projection method with an inertial technique for split feasibility problems in Banach spaces with applications to image restoration problems. J Fixed Point Theory Appl. 2019;21:33.
   Web of Science ®Google Scholar
• Thong DV, Hieu DV. An inertial method for solving split common fixed point problems. J Fixed Point Theory Appl. 2017;19:3029–3051.
   Web of Science ®Google Scholar
• Suantai S, Pholasa N, Cholamjiak P. Relaxed CQ algorithms involving the inertial technique for multiple-sets split feasibility problems. RACSAM. 2019;113:1081–1099.
   Google Scholar
• Nakajo K, Takahashi W. Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. J Math Anal Appl. 2003;279:372–379.
   Web of Science ®Google Scholar
• Wang F, Xu HK. Cyclic algorithms for split feasibility problems in Hilbert spaces. Nonlinear Anal. 2011;74(12):4105–4111.
   Web of Science ®Google Scholar
• Gornicki J. Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces. Comment Math Univ Carolin. 1998;301:249–252.
   Google Scholar
• Zarantonello EH. Projections on convex sets in Hilbert space and spectral theory. Contributions to nonlinear functional analysis. New York: American Academic Press; 1971. p. 19–32.
   Google Scholar
• Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. New York: Springer; 2011. (CMS Books in Mathematics).
   Google Scholar
• Shehu Y, Iyiola OS, Enyi CD. An iterative algorithm for solving split feasibility problems and fixed point problems in Banach spaces. Numer Algor. 2016;72:835–864.
   Web of Science ®Google Scholar
• Moudafi A. Alternating CQ-algorithms for convex feasibility and split fixed-point problems. J Nonlinear Convex A. 2014;15:809–818.
   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
• Dong QL, He S, Zhao J. Solving the split equality problem without prior knowledge of operator norms. Optim. 2015;64(9):1887–1906.
   Web of Science ®Google Scholar
• Wang F. On the convergence of CQ algorithm with variable steps for the split equality problem. Numer Algor. 2017;74:927–935.
   Web of Science ®Google Scholar
• Zhao J. Solving split equality fixed-point problem of quasi-nonexpansive mappings without prior knowledge of operators norms. Optim. 2015;64(12):2619–2630.
   Web of Science ®Google Scholar