New subgradient extragradient methods for common solutions to equilibrium problems
In this paper, three parallel hybrid subgradient extragradient algorithms are proposed for finding a common solution of a finite family of equilibrium problems in Hilbert spaces. The proposed algorithms originate from previously known results for variational inequalities and can be considered as mod...
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| Veröffentlicht in: | Computational optimization and applications Jg. 67; H. 3; S. 571 - 594 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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01.07.2017
Springer Nature B.V |
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| ISSN: | 0926-6003, 1573-2894 |
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| Abstract | In this paper, three parallel hybrid subgradient extragradient algorithms are proposed for finding a common solution of a finite family of equilibrium problems in Hilbert spaces. The proposed algorithms originate from previously known results for variational inequalities and can be considered as modifications of extragradient methods for equilibrium problems. Theorems of strong convergence are established under the standard assumptions imposed on bifunctions. Some numerical experiments are given to illustrate the convergence of the new algorithms and to compare their behavior with other algorithms. |
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| AbstractList | In this paper, three parallel hybrid subgradient extragradient algorithms are proposed for finding a common solution of a finite family of equilibrium problems in Hilbert spaces. The proposed algorithms originate from previously known results for variational inequalities and can be considered as modifications of extragradient methods for equilibrium problems. Theorems of strong convergence are established under the standard assumptions imposed on bifunctions. Some numerical experiments are given to illustrate the convergence of the new algorithms and to compare their behavior with other algorithms. |
| Author | Van Hieu, Dang |
| Author_xml | – sequence: 1 givenname: Dang surname: Van Hieu fullname: Van Hieu, Dang email: dv.hieu83@gmail.com organization: Department of Mathematics, Vietnam National University |
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| CitedBy_id | crossref_primary_10_1080_00036811_2018_1460816 crossref_primary_10_1080_02331934_2021_1873988 crossref_primary_10_1007_s13398_020_00827_1 crossref_primary_10_1007_s40314_022_01817_2 crossref_primary_10_1007_s10589_020_00258_z crossref_primary_10_3846_mma_2019_001 crossref_primary_10_1007_s13398_018_0595_8 crossref_primary_10_1007_s40314_025_03428_z crossref_primary_10_1007_s10898_024_01377_1 crossref_primary_10_1007_s10957_025_02764_8 crossref_primary_10_1007_s12215_021_00608_8 crossref_primary_10_1007_s41478_024_00752_1 crossref_primary_10_1007_s12215_022_00845_5 crossref_primary_10_1002_mma_5703 crossref_primary_10_1007_s11075_018_0532_0 crossref_primary_10_1007_s00186_018_0640_6 |
| Cites_doi | 10.1007/BF02192244 10.1016/j.jmaa.2006.08.036 10.1007/s10013-015-0129-z 10.1016/0362-546X(92)90159-C 10.1080/00036811.2013.872777 10.1080/02331930601122876 10.1109/TPWRS.2003.820692 10.1007/s11228-011-0192-x 10.1007/s12190-014-0801-6 10.1137/S0036144593251710 10.1080/02331934.2012.759327 10.1515/9781400873173 10.1007/s10957-012-0085-7 10.4134/JKMS.2015.52.2.373 10.1007/s10898-011-9693-2 10.3846/13926292.2016.1183527 10.1007/s10957-010-9757-3 10.1007/s11075-015-0092-5 10.1080/10556788.2010.551536 10.1007/BF02614504 10.1002/mma.4286 10.1016/S1076-5670(08)70157-5 10.1017/CBO9780511526152 10.1007/s10589-011-9401-7 |
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| DOI | 10.1007/s10589-017-9899-4 |
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| Keywords | Hybrid method Equilibrium problem Parallel computation Extragradient method 47H05 47J25 65J15 65Y05 Subgradient method 91B50 |
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| Snippet | In this paper, three parallel hybrid subgradient extragradient algorithms are proposed for finding a common solution of a finite family of equilibrium problems... |
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| SubjectTerms | Algorithms Convergence Convex and Discrete Geometry Equilibrium Equilibrium methods Inequalities Management Science Mathematics Mathematics and Statistics Operations Research Operations Research/Decision Theory Optimization Statistics |
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| Title | New subgradient extragradient methods for common solutions to equilibrium problems |
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