A parallel subgradient projection algorithm for quasiconvex equilibrium problems under the intersection of convex sets

In this paper, we studied the equilibrium problem where the bi-function may be quasiconvex with respect to the second variable and the feasible set is the intersection of a finite number of convex sets. We propose a projection algorithm, where the projection can be computed independently onto each c...

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Veröffentlicht in:Optimization Jg. 71; H. 15; S. 4447 - 4462
Hauptverfasser: Yen, Le Hai, Muu, Le Dung
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Taylor & Francis 09.12.2022
Taylor & Francis LLC
Schlagworte:
Algorithms
Computational geometry
Convexity
Equilibria
intersection
Intersections
Mathematical analysis
Operators (mathematics)
projection method
quasiconvexity
subgradient method
ISSN:0233-1934, 1029-4945
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Abstract In this paper, we studied the equilibrium problem where the bi-function may be quasiconvex with respect to the second variable and the feasible set is the intersection of a finite number of convex sets. We propose a projection algorithm, where the projection can be computed independently onto each component set. The convergence of the algorithm is investigated and numerical examples for a variational inequality problem involving affine fractional operator are provided to demonstrate the behaviour of the algorithm.
AbstractList In this paper, we studied the equilibrium problem where the bi-function may be quasiconvex with respect to the second variable and the feasible set is the intersection of a finite number of convex sets. We propose a projection algorithm, where the projection can be computed independently onto each component set. The convergence of the algorithm is investigated and numerical examples for a variational inequality problem involving affine fractional operator are provided to demonstrate the behaviour of the algorithm.
Author Muu, Le Dung
Yen, Le Hai
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  organization: Institute of Mathematics, VAST
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  givenname: Le Dung
  surname: Muu
  fullname: Muu, Le Dung
  organization: TIMAS, Thang Long University and Institute of Mathematics, VAST
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Cites_doi 10.1137/040606958
10.1080/02331939708844364
10.1080/02331934.2016.1195831
10.1007/s10898-018-00735-0
10.1007/978-1-4613-3341-8_1
10.1007/s10957-017-1176-2
10.1016/0362-546X(92)90159-C
10.1007/978-981-13-3059-9_6
10.1080/01630569808816813
10.1137/0328046
10.1080/02331934.2016.1182528
10.1080/02331934.2016.1189551
10.1080/1055678031000111236
10.1007/s10589-011-9450-y
10.2140/pjm.1955.5.807
10.1080/02331930601122876
10.1007/s11228-017-0451-6
10.1007/978-3-030-00205-3
10.1007/s11590-013-0612-y
10.1007/s10092-019-0308-5
10.1007/978-1-4613-3326-5
10.1016/j.ejor.2009.07.006
10.1007/s40305-017-0156-4
10.1007/PL00011414
10.1016/j.ejor.2012.11.037
10.1016/j.orl.2020.07.007
10.1007/s10957-009-9529-0
10.1080/02331934.2015.1080702
10.1051/ro/2017078
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References CIT0030
CIT0010
CIT0031
CIT0012
Iusem AN. (CIT0032) 1998; 5
CIT0034
CIT0011
CIT0033
He B. (CIT0038) 1995; 25
CIT0014
CIT0036
CIT0013
CIT0016
Penot J-P (CIT0026) 2000; 7
CIT0037
CIT0018
CIT0017
CIT0039
CIT0019
Mangasarian O. (CIT0023) 1969
CIT0040
CIT0021
CIT0001
CIT0022
Duc PM (CIT0035) 2016; 12
Greenberg HP (CIT0027) 1973; 15
Blum E (CIT0003) 1994; 62
Kassay G (CIT0020) 2018
CIT0025
CIT0002
CIT0024
CIT0005
Santos P (CIT0015) 2011; 30
CIT0004
CIT0007
CIT0029
CIT0006
CIT0028
CIT0009
CIT0008
References_xml – ident: CIT0007
  doi: 10.1137/040606958
– ident: CIT0037
  doi: 10.1080/02331939708844364
– volume: 5
  start-page: 269
  year: 1998
  ident: CIT0032
  publication-title: Convex Anal
– volume-title: Nonlinear programming
  year: 1969
  ident: CIT0023
– ident: CIT0036
  doi: 10.1080/02331934.2016.1195831
– ident: CIT0018
  doi: 10.1007/s10898-018-00735-0
– ident: CIT0025
  doi: 10.1007/978-1-4613-3341-8_1
– ident: CIT0017
  doi: 10.1007/s10957-017-1176-2
– ident: CIT0004
  doi: 10.1016/0362-546X(92)90159-C
– ident: CIT0008
  doi: 10.1007/978-981-13-3059-9_6
– ident: CIT0030
  doi: 10.1080/01630569808816813
– ident: CIT0006
– volume: 7
  start-page: 243
  year: 2000
  ident: CIT0026
  publication-title: J Convex Anal
– ident: CIT0040
  doi: 10.1137/0328046
– ident: CIT0016
  doi: 10.1080/02331934.2016.1182528
– volume-title: Equilibrium problems and applications. Series Mathematics in Science and Engineering
  year: 2018
  ident: CIT0020
– ident: CIT0028
  doi: 10.1080/02331934.2016.1189551
– ident: CIT0033
  doi: 10.1080/1055678031000111236
– ident: CIT0012
  doi: 10.1007/s10589-011-9450-y
– ident: CIT0005
  doi: 10.2140/pjm.1955.5.807
– ident: CIT0014
  doi: 10.1080/02331930601122876
– ident: CIT0021
  doi: 10.1007/s11228-017-0451-6
– volume: 25
  start-page: 939
  year: 1995
  ident: CIT0038
  publication-title: Sci China (Series A)
– volume: 15
  start-page: 437
  year: 1973
  ident: CIT0027
  publication-title: Cahiers Centre Études Recherche Oper
– ident: CIT0002
  doi: 10.1007/978-3-030-00205-3
– ident: CIT0034
  doi: 10.1007/s11590-013-0612-y
– ident: CIT0009
  doi: 10.1007/s10092-019-0308-5
– ident: CIT0031
  doi: 10.1007/978-1-4613-3326-5
– ident: CIT0039
  doi: 10.1016/j.ejor.2009.07.006
– ident: CIT0010
  doi: 10.1007/s40305-017-0156-4
– ident: CIT0029
  doi: 10.1007/PL00011414
– volume: 30
  start-page: 91
  year: 2011
  ident: CIT0015
  publication-title: Comput Appl Math
– ident: CIT0024
– ident: CIT0001
  doi: 10.1016/j.ejor.2012.11.037
– ident: CIT0022
  doi: 10.1016/j.orl.2020.07.007
– ident: CIT0011
  doi: 10.1007/s10957-009-9529-0
– ident: CIT0019
  doi: 10.1080/02331934.2015.1080702
– volume: 12
  start-page: 833
  issue: 4
  year: 2016
  ident: CIT0035
  publication-title: Pacific J Optim
– ident: CIT0013
  doi: 10.1051/ro/2017078
– volume: 62
  start-page: 127
  year: 1994
  ident: CIT0003
  publication-title: Math Student
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SubjectTerms Algorithms
Computational geometry
Convexity
Equilibria
intersection
Intersections
Mathematical analysis
Operators (mathematics)
projection method
quasiconvexity
subgradient method
Title A parallel subgradient projection algorithm for quasiconvex equilibrium problems under the intersection of convex sets
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