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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 72, 2023 - Issue 10
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Research Article

An alternated inertial general splitting method with linearization for the split feasibility problem

ORCID Icon, , &
Pages 2585-2607 | Received 05 Jan 2021, Accepted 12 Apr 2022, Published online: 06 May 2022

References

  • Censor Y, Elfving T. A multiprojection algorithm using Bregman projections in a product space. Numer Algorithms. 1994;8:221–239.
  • 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.
  • Byrne CL. Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Probl. 2002;18:441–453.
  • Yen LH, Huyen NTT, Muu LD. A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models. J Global Optim. 2019;73:849–868.
  • Yen LH, Muu LD, Huyen NTT. An algorithm for a class of split feasibility problems: application to a model in electricity production. Math Methods Oper Res. 2016;84:549–565.
  • Byrne CL. A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Probl. 2004;20:103–120.
  • Cho SY. A convergence theorem for generalized mixed equilibrium problems and multivalued asymptotically nonexpansive mappings. J Nonlinear Convex Anal. 2020;21:1017–1026.
  • Dong QL, Yao Y, He S. Weak convergence theorems of the modified relaxed projection algorithms for the split feasibility problem in Hilbert spaces. Optim Lett. 2014;8:1031–1046.
  • Gibali A, Liu L, Tang YC. Note on the modified relaxation CQ algorithm for the split feasibility problem. Optim Lett. 2018;12:817–830.
  • He S, Xu HK. The selective projection method for convex feasibility and split feasibility problems. J Nonlinear Sci Appl. 2018;19(7):1199–1215.
  • Tan B, Cho SY. Strong convergence of inertial forwardbackward methods for solving monotone inclusions. Appl Anal. 2021. doi:10.1080/00036811.2021.1892080
  • Wang F. Polyak's gradient method for split feasibility problem constrained by level sets. Numer Algorithms. 2018;77:925–938.
  • Zhao J, Zong H. Iterative algorithms for solving the split feasibility problem in Hilbert spaces. J Fixed Point Theory Appl. 2018;20:11.
  • López G, Martín-Márquez V, Wang F, et al. Solving the split feasibility problem without prior knowledge of matrix norms. Inverse Probl. 2012;28(8):373–389.
  • Dong QL, He S, Rassias MT. General splitting methods with linearization for the split feasibility problem. J Global Optim. 2021;79:813–836.
  • Polyak BT. Some methods of speeding up the convergence of iteration methods. USSR Comput Math Math Phys. 1964;4:1–17.
  • Nesterov YE. A method for solving the convex programming problem with convergence rate O(1/k2). Dokl Akad Nauk SSSR. 1983;269:43–547.
  • Beck A, Teboulle M. A fast iterative shrinkage–thresholding algorithm for linear inverse problems. SIAM J Imaging Sci. 2009;2(1):183–202.
  • Iyiola OS, Ogbuisi FU, Shehu Y. An inertial type iterative method with Armijo linesearch for nonmonotone equilibrium problems. Calcolo. 2018;55(4):1–22.
  • Shehu Y, Iyiola OS, Thong DV, et al. An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Math Method Oper Res. 2021;93:213–242.
  • Shehu Y, Iyiola OS, Ogbuisi FU. Iterative methods with inertial terms for nonexpansive mappings: application to compressed sensing. Numer Algorithm. 2020;83:1321–1347.
  • Dang Y, Sun J, Xu H. Inertial accelerated algorithms for solving a split feasibility problem. J Ind Manag Optim. 2017;13:1383–1394.
  • Gibali A, Mai DT, Vinh NT. A new relaxed CQ algorithm for solving split feasibility problems in Hilbert spaces and its applications. J Ind Manag Optim. 2019;15:963–984.
  • Suantai S, Pholasa N, Cholamjiak P. The modified inertial relaxed CQ algorithm for solving the split feasibility problems. J Ind Manag Optim. 2018;14:1595–1615.
  • Malitsky Y, Pock T. A first-order primal-dual algorithm with linesearch. SIAM J Optim. 2018;28:411–432.
  • Mu Z, Peng Y. A note on the inertial proximal point method. Stat Optim Inf Comput. 2015;3:241–248.
  • Iutzeler F, Malick J. On the proximal gradient algorithm with alternated inertia. J Optim Theory Appl. 2018;176:688–710.
  • Shehu Y, Iyiola OS. Projection methods with alternating inertial steps for variational inequalities: weak and linear convergence. Appl Numer Math. 2020;157:315–337.
  • Shehu Y, Dong QL, Liu L. Global and linear convergence of alternated inertial methods for split feasibility problems. RACSAM. 2021;115:53.
  • Shehu Y, Gibali A. New inertial relaxed method for solving split feasibilities. Optim Lett. 2021;15:2109–2126.
  • Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. 2nd ed. Berlin: Springer; 2017.
  • Goebel K, Reich S. Uniform convexity, hyperbolic geometry, and nonexpansive mappings. New York and Basel: Marcel Dekker: 1984.
  • Dong QL, Tang YC, Cho YJ, et al. ‘Optimal’ choice of the step length of the projection and contraction methods for solving the split feasibility problem. J Global Optim. 2018;71:341–360.
  • Tibshirani R. Regression shrinkage and selection via the lasso. J R Stat Soc Ser B Stat Methodol. 1996;58:267–288.

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