Geodesic
Parallel projected subgradient method for solving split system of fixed point set constraint equilibrium problems in Hilbert spaces
Novi Sad Journal of Mathematics, Tome 50 (2020) no. 2.

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In this paper, we propose two strongly convergent algorithms which combines Mann iterative scheme, diagonal subgradient method, projection method and proximal method for solving split system of fixed point set constrained equilibrium problems in real Hilbert spaces. The computation of first algorthim requires prior knowledge of operator norm. The problem of finding or at least an estimate of the norm of an operator, in general, is not an easy task in Hilbert spaces. Based on the first algorithm, we propose another algorithm with a way of selecting the step-sizes such that its implementation does not need any prior information about the operator norm. The strong convergence properties of the algorithms are established under mild assumptions on equilibrium bifunctions.
Publié le :
DOI : 10.30755/NSJOM.09298
Classification : 68W10, 47J25, 47H00, 90C25, 65K10
Keywords: Split fixed point problem, split equilibrium problem, pseudomonotone bifunction, parallel projection, diagonal subgradient method 
@article{10.30755/NSJOM.09298,
     author = {Anteneh Getachew Gebrie and Rabian Wangkeeree},
     title = {Parallel projected subgradient method for solving split system of fixed point
set constraint equilibrium problems in {Hilbert} spaces},
     journal = {Novi Sad Journal of Mathematics},
     pages = {7 - 33},
     publisher = {mathdoc},
     volume = {50},
     number = {2},
     year = {2020},
     doi = {10.30755/NSJOM.09298},
     url = {http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.09298/}
}
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Anteneh Getachew Gebrie; Rabian Wangkeeree. Parallel projected subgradient method for solving split system of fixed point
set constraint equilibrium problems in Hilbert spaces. Novi Sad Journal of Mathematics, Tome 50 (2020) no. 2. doi : 10.30755/NSJOM.09298. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.09298/

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