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2016 | Vol. 22, nr 1 | 81--89
Tytuł artykułu

Iterative algorithm for the split equality problem in Hilbert spaces

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we studied the split equality problems (SEP) with a new proposed iterative algorithm and established the strong convergence of the proposed algorithm to solution of the split equality problems (SEP).
Wydawca

Rocznik
Strony
81--89
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
  • Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria
Bibliografia
  • [1] A. Aleyner and S. Reich, Block-iterative algorithms for solving convex feasibility problem in Hilbert and Banach, J. Math. Anal. Appl. 343 (2008), no. 1, 427-435.
  • [2] H. Attouch, J. Bolte, P. Redont and A. Soubeyran, Alternating proximal algorithms for weakly coupled minimization problems. Applications to dynamical games and PDEs, J. Convex Anal. 15 (2008), no. 3, 485-506.
  • [3] H. H. Bauschke and j. M. Borwein, On projection algorithms for solving convex feasibility problems, SIAM Rev. 38 (1996), 367-426,
  • [4] C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems 18 (2002), 441-453.
  • [5] C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems 20 (2004), 103-120.
  • [6] C. Byrne and A. Moudafi, Extensions of the CQ algorithm for the split feasibility and split equality problems, preprint (2013), https://hal-uag.archives-ouvertes.fr/hal-00776640.
  • [7] Y. Censor, T. Bortfeld, B. Martin and A. Trofimov, A unified approach for inversion problems in intensity-modulated radiation therapy, Phys. Med. Biol. 51 (2006), no. 10, 2353-2365.
  • [8] Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms 8 (1994), 221-239.
  • [9] P. L. Combettes and J. C. Pesquet, Proximal splitting methods in signal processing, in: Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer Optim. Appl. 49, Springer, New York (2011), 185-212.
  • [10] Q. Dong, S. He and J. Zhao, Solving the split equality problem without prior knowledge of operator norms, Optimization 64 (2015), DOI 10.1080/02331934.2014.895897.
  • [11] S. He and W. Zhu, A note on approximating curve with 1-norm regularization method for the split feasibility problem, J. Appl. Math. 2012 (2012), Article ID 683890.
  • [12] Z. Li, D. Dan and W. Zhang, A self-adaptive projection-type method for nonlinear multiplesets split feasibibilty problem, Inverse Probl. Sci. Eng. 20 (2013), 155-170.
  • [13] G. Lopez, V. Martin-Marquez, F. Wang and H. K. Xu, Solving the split feasibility problem without prior knowledge of matrix norms, Inverse Problems 28 (2012), no. 8, Article ID 085004.
  • [14] A. Moudafi, Alternating CQ-algorithms for convex feasibility and split fixed-point problems, J. Nonlinear Convex Anal. 15 (2014), no. 4, 809-818.
  • [15] D. Pascali and S. Sburlan, Nonlinear Mappings of Monotone Type, Editura Academiei, Bucharest, 1978.
  • [16] P. Tseng, A modified forward-backward splitting method for maximal monotone mappings, SIAMj. Control Optim. 28 (2000), no. 2, 431-446.
  • [17] H. K. Xu, Iterative algorithms for nonlinear operators, J. Lond. Math. Soc. (2) 66 (2002), no. 1, 240-256.
  • [18] Q. Yang, The relaxed CQ algorithm for soloving the split feasibility problem, Inverse Problems 20 (2004), 1261-1266.
  • [19] J. Zhao, J. Zhang and Q. Yang, Asimple projection method for solving the multiple-sets split feasibility problem, Inverse Probl. Sci. Eng. 21 (2013), 537-546.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
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