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Abstrakty
The purpose of this article is to study and analyse a new extragradient-type algorithm with an inertial extrapolation step for solving split fixed-point problems for demicontractive mapping, equilibrium problem, and pseudomonotone variational inequality problem in real Hilbert spaces. One of the advantages of the proposed algorithm is that a strong convergence result is achieved without a prior estimate of the Lipschitz constant of the cost operator, which is very difficult to find. In addition, the stepsize is generated at each iteration by some simple computations, which allows it to be easily implemented without the prior knowledge of the Lipschitz constant of the cost operator. Some numerical experiments are reported to show the performance and behaviour of the sequence generated by our algorithm. The obtained results in this article extend and improve many related recent results in this direction in the literature.
Wydawca
Czasopismo
Rocznik
Tom
Strony
506--527
Opis fizyczny
Bibliogr. 37 poz., tab., wykr.
Twórcy
autor
- School of Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa
autor
- Department of Mathematics, University of Eswatini, Private Bag 4, Kwaluseni, Eswatini
- Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94 Medunsa 0204, Pretoria, South Africa
autor
- Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94 Medunsa 0204, Pretoria, South Africa
- Federal University of Agriculture, Abeokuta, Nigeria
Bibliografia
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- [10] G. M. Korpelevich, The extragradient method for finding saddle points and other problems, Ekonomika Mat. Metody 12 (1976), 747–756.
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- [14] N. Nadezhkina and W. Takahashi, Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 128 (2006), 191–201.
- [15] M. V. Solodov and B. F. Svaiter, A new projection method for variational inequality problems, SIAM J. Control Optim. 37 (1999), 765–776.
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- [17] Y. Yao, G. Marino, and L. Muglia, A modified Korpelevich’s method convergent to minimum-norm solution of a variational inequality, Optimization 63 (2014), 559–569.
- [18] Y. Censor, A. Gibali, and S. Reich, The subgradient extragradient method for solving variational inequalities in Hilbert space, J. Optim. Theory Appl. 148 (2011), 318–335.
- [19] Y. Censor, A. Gibali, and S. Reich, Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space, Optim. Meth. Softw. 26 (2011), 827–845.
- [20] Y. Censor, A. Gibali, and S. Reich, Extensions of Korpelevichas extragradient method for the variational inequality problem in Euclidean space, Optimization 61 (2012), 1119–1132.
- [21] A. Gibali, A new non-Lipschitzian projection method for solving variational inequalities in Euclidean spaces, J. Nonlinear Anal. Optim. 6 (2015), 41–51.
- [22] Y. Shehu and O. S. Iyiola, Strong convergence result for monotone variational inequalities, Numer. Algor. 76 (2017), 259–282, DOI: https://doi.org/10.1007/s11075-016-0253-1.
- [23] Y. Censor and Y. Segal, The split common fixed-point for directed operators, J. Convex Anal. 16 (2009), 587–600.
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- [28] Y. Shehu and F. U. Ogbuisi, An iterative algorithm for approximating a solution of split common fixed-point problem for demicontractive maps, Dynam. Cont. Dis. Ser. B 23 (2012), 225–240.
- [29] A. Hanjing and S. Suantai, Hybrid inertial accelerated algorithms for split fixed-point problems of demicontractive mappings and equilibrium problems, Numer. Algor. 85 (2020), 1051–1073, DOI: https://doi.org/10.1007/s11075-019-00855-y.
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- [33] H. Cui and F. Wang, Iterative methods for the split common fixed-point problem in a Hilbert spaces, Fixed Point Theory Appl. 2014 (2014), 78.
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Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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