Regularization methods for solving the split feasibility problem with multiple output sets in Hilbert spaces
DOI:
https://doi.org/10.12775/TMNA.2022.020Słowa kluczowe
Hilbert space, metric projection, regularization, split feasibility problemAbstrakt
We study the split feasibility problem with multiple output sets in Hilbert spaces. In order to solve this problem, we introduce several new iterative processes by using the Tikhonov regularization method.Bibliografia
Y. Alber and I. Ryazantseva, Nonlinear Ill-Posed Problems of Monotone Type, Springer, Dordrecht, 2006.
D. Butnariu and E. Resmerita, Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces, Abstr. Appl. Anal. 2006 (2006), 1–39.
C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems 18 (2002), 441–453.
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems 18 (2004), 103–120.
C. Byrne, Y. Censor, A. Gibali and S. Reich, The split common null point problem, J. Nonlinear Convex Anal. 13 (2012), 759–775.
Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms 8 (1994), 221–239.
Y. Censor, T. Elfving, N. Kopf and T. Bortfeld, The multiple-sets split feasibility problem and its application, Inverse Problems 21 (2005), 2071–2084.
Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problems, Numer. Algorithms 59 (2012), 301–323.
V. Dadashi, Shrinking projection algorithms for the split common null point problem, Bull. Aust. Math. Soc. 99 (2017), 299–306.
G.Z. Eskandani, M. Raeisi and T.M. Rassias, A hybrid extragradient method for solving pseudomonotone equilibrium problems using Bregman distance, J. Fixed Point Theory Appl. 20 (2018), 132.
K. Goebel and W.A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Stud. Adv. Math., vol. 28, Cambridge Univ. Press, Cambridge, UK, 1990.
K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker, New York, 1984.
G.J. Minty, Monotone (non-linear) operators in Hilbert space, Duke Math. J. 2 (1962), 341–346.
S. Reich, Extension problems for accretive sets in Banach spaces, J. Functional Anal. 26 (1977), 378–395.
S. Reich, M.T. Truong and T.N.H. Mai, The split feasibility problem with multiple output sets in Hilbert spaces, Optim. Lett. 14 (2020), 2335–2353.
S. Reich, T.M. Tuyen and M.T.N. Ha, An optimization approach to solving the split feasibility problem in Hilbert spaces, J. Global Optim. 79 (2021), 837–852.
R.T. Rockafellar, On the maximal monotonicity of subdifferential mappings, Pacific J. Math. 33 (1970), 209–216.
S. Takahashi and W. Takahashi, The split common null point problem and the shrinking projection method in Banach spaces, Optimization 65 (2016), 281–287.
W. Takahashi, The split feasibility problem and the shrinking projection method in Banach spaces, J. Nonlinear Convex Anal. 16 (2015), 1449–1459.
W. Takahashi, The split common null point problem in Banach spaces, Arch. Math. 104 (2015), 357–365.
F. Wang and H.-K. Xu, Cyclic algorithms for split feasibility problems in Hilbert spaces, Nonlinear Anal. 74 (2011), 4105–4111.
H.-K. Xu, Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006), 631–643.
H.-K. Xu, A variable Krasnosel’skiı̆–Mann algorithm and the multiple-set split feasibility problem, Inverse Problems 22 (2006), 2021–2034.
H.-K. Xu, Iterative methods for the split feasibility problem in infinite dimensional Hilbert spaces, Inverse Problems 26 (2010), 105018.
Q. Yang, The relaxed CQ algorithm for solving the split feasibility problem, Inverse Problems 20 (2004), 1261–1266.
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Prawa autorskie (c) 2022 Simeon Reich, Truong Minh Tuyen
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