An extragradient algorithm for solving bilevel pseudomonotone variational inequalities
We present an extragradient-type algorithm for solving bilevel pseudomonone variational inequalities. The proposed algorithm uses simple projection sequences. Under mild conditions, the convergence of the iteration sequences generated by the algorithm is obtained.
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| Published in | Journal of global optimization Vol. 52; no. 3; pp. 627 - 639 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.03.2012
Springer Nature B.V |
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| Online Access | Get full text |
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| Abstract | We present an extragradient-type algorithm for solving bilevel pseudomonone variational inequalities. The proposed algorithm uses simple projection sequences. Under mild conditions, the convergence of the iteration sequences generated by the algorithm is obtained. |
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| AbstractList | We present an extragradient-type algorithm for solving bilevel pseudomonone variational inequalities. The proposed algorithm uses simple projection sequences. Under mild conditions, the convergence of the iteration sequences generated by the algorithm is obtained. We present an extragradient-type algorithm for solving bilevel pseudomonone variational inequalities. The proposed algorithm uses simple projection sequences. Under mild conditions, the convergence of the iteration sequences generated by the algorithm is obtained.[PUBLICATION ABSTRACT] |
| Author | Anh, P. N. Kim, J. K. Muu, L. D. |
| Author_xml | – sequence: 1 givenname: P. N. surname: Anh fullname: Anh, P. N. organization: Department of Mathematics, Kyungnam University – sequence: 2 givenname: J. K. surname: Kim fullname: Kim, J. K. organization: Department of Mathematics, Kyungnam University – sequence: 3 givenname: L. D. surname: Muu fullname: Muu, L. D. email: ldmuu@math.ac.vn organization: Institute of Mathematics |
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| Cites_doi | 10.1080/02331930601122876 10.1007/978-94-011-1026-6 10.1007/BF00121270 10.1016/S0362-546X(01)00201-2 10.1007/s10957-004-0926-0 10.1017/CBO9780511983658 10.1007/b101835 10.1016/j.na.2011.05.091 10.1007/s10898-009-9476-1 10.1007/s10898-010-9551-7 10.1016/j.cam.2005.04.004 10.1007/s10898-008-9355-1 10.1016/j.jmaa.2004.11.017 10.1007/978-1-4613-0239-1 10.1016/j.amc.2010.01.087 10.15388/NA.2009.14.1.14528 10.1155/2007/38752 |
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| Keywords | Bilevel variational inequality Global convergence Extragradient algorithm 90 C25 Pseudomonotonicity 65 K10 Lipschitz continuity |
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| References | Bakushinskii, Goncharskii (CR8) 1994 Muu, Quoc, Nguyen (CR20) 2008; 57 Anh, Muu, Strodiot (CR4) 2009; 34 Kalashnikov, Kalashnikova (CR13) 1996; 8 Hung, Muu (CR12) 2011; 74 Moudafi (CR21) 2010; 47 Konnov, Kum (CR15) 2001; 47 Anh, Muu, Hien, Strodiot (CR5) 2005; 124 Tikhonov, Arsenin (CR24) 1977 Konnov (CR17) 2009; 10 Konnov, Ali (CR16) 2006; 188 Anh (CR2) 2009; 14 Xu, Li, Yang (CR25) 2009; 44 Baiocchi, Capelo (CR6) 1984 Solodov (CR22) 2007; 14 Suzuki (CR23) 2005; 305 Anh (CR1) 2008; 10 Daniele, Giannessi, Maugeri (CR9) 2003 Bakushinskii, Polyak (CR7) 1974; 219 CR27 CR26 Konnov, Dyabilkin (CR18) 2011; 49 Giannessi, Maugeri, Pardalos (CR11) 2004 Facchinei, Pang (CR10) 2003 Anh, Hien (CR3) 2010; 12 Konnov (CR14) 2000 Luo, Pang, Ralph (CR19) 1996 L.D. Muu (9870_CR20) 2008; 57 V.V. Kalashnikov (9870_CR13) 1996; 8 I.V. Konnov (9870_CR17) 2009; 10 P.N. Anh (9870_CR1) 2008; 10 I.V. Konnov (9870_CR14) 2000 Z.Q. Luo (9870_CR19) 1996 P.N. Anh (9870_CR5) 2005; 124 F. Facchinei (9870_CR10) 2003 A.N. Tikhonov (9870_CR24) 1977 M. Solodov (9870_CR22) 2007; 14 P.N. Anh (9870_CR3) 2010; 12 C. Baiocchi (9870_CR6) 1984 9870_CR26 P.G. Hung (9870_CR12) 2011; 74 9870_CR27 P.N. Anh (9870_CR2) 2009; 14 A.B. Bakushinskii (9870_CR8) 1994 T. Suzuki (9870_CR23) 2005; 305 I.V. Konnov (9870_CR16) 2006; 188 I.V. Konnov (9870_CR18) 2011; 49 I.V. Konnov (9870_CR15) 2001; 47 M.H. Xu (9870_CR25) 2009; 44 P.N. Anh (9870_CR4) 2009; 34 A. Moudafi (9870_CR21) 2010; 47 P. Daniele (9870_CR9) 2003 A.B. Bakushinskii (9870_CR7) 1974; 219 F. Giannessi (9870_CR11) 2004 |
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Theory Methods Appl. doi: 10.1016/S0362-546X(01)00201-2 contributor: fullname: I.V. Konnov – ident: 9870_CR27 doi: 10.1016/j.amc.2010.01.087 – volume: 14 start-page: 27 year: 2009 ident: 9870_CR2 publication-title: Nonlinear Anal. Forum doi: 10.15388/NA.2009.14.1.14528 contributor: fullname: P.N. Anh – volume: 74 start-page: 6121 year: 2011 ident: 9870_CR12 publication-title: Nonlinear Anal. Theory Methods Appl. doi: 10.1016/j.na.2011.05.091 contributor: fullname: P.G. Hung – volume-title: Mathematical Programs with Equilibrum Constraints year: 1996 ident: 9870_CR19 doi: 10.1017/CBO9780511983658 contributor: fullname: Z.Q. Luo – volume: 44 start-page: 535 year: 2009 ident: 9870_CR25 publication-title: J. Glob. Optim. doi: 10.1007/s10898-008-9355-1 contributor: fullname: M.H. Xu – volume: 305 start-page: 227 year: 2005 ident: 9870_CR23 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2004.11.017 contributor: fullname: T. Suzuki – volume: 12 start-page: 49 year: 2010 ident: 9870_CR3 publication-title: East–West J. Math. contributor: fullname: P.N. Anh – volume: 124 start-page: 285 year: 2005 ident: 9870_CR5 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-004-0926-0 contributor: fullname: P.N. Anh – volume-title: Equilibrium Problems and Variational Models year: 2003 ident: 9870_CR9 doi: 10.1007/978-1-4613-0239-1 contributor: fullname: P. Daniele – volume-title: Variational and Quasivariational Inequalities, Applications to Free Boundary Problems year: 1984 ident: 9870_CR6 contributor: fullname: C. Baiocchi – volume: 47 start-page: 287 year: 2010 ident: 9870_CR21 publication-title: J. Glob. Optim. doi: 10.1007/s10898-009-9476-1 contributor: fullname: A. Moudafi – ident: 9870_CR26 doi: 10.1155/2007/38752 – volume: 49 start-page: 575 year: 2011 ident: 9870_CR18 publication-title: J. Glob. Optim. doi: 10.1007/s10898-010-9551-7 contributor: fullname: I.V. Konnov – volume-title: Combined Relaxation Methods for Variational Inequalities year: 2000 ident: 9870_CR14 contributor: fullname: I.V. Konnov – volume: 14 start-page: 227 year: 2007 ident: 9870_CR22 publication-title: J. Convex Anal. contributor: fullname: M. Solodov – volume: 34 start-page: 67 year: 2009 ident: 9870_CR4 publication-title: ACTA Mathematica Vietnamica contributor: fullname: P.N. Anh – volume-title: Solutions of Ill-Posed Problems year: 1977 ident: 9870_CR24 contributor: fullname: A.N. Tikhonov – volume: 10 start-page: 81 year: 2008 ident: 9870_CR1 publication-title: East–West J. Math. contributor: fullname: P.N. Anh – volume: 188 start-page: 165 year: 2006 ident: 9870_CR16 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2005.04.004 contributor: fullname: I.V. Konnov – volume: 219 start-page: 1038 year: 1974 ident: 9870_CR7 publication-title: Sovjet Mathematics Dokl. contributor: fullname: A.B. Bakushinskii – volume: 8 start-page: 289 year: 1996 ident: 9870_CR13 publication-title: J. Glob. Optim. doi: 10.1007/BF00121270 contributor: fullname: V.V. Kalashnikov – volume: 10 start-page: 93 year: 2009 ident: 9870_CR17 publication-title: J. Nonlinear Convex Anal. contributor: fullname: I.V. Konnov |
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| Snippet | We present an extragradient-type algorithm for solving bilevel pseudomonone variational inequalities. The proposed algorithm uses simple projection sequences.... |
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| SubjectTerms | Algorithms Computer Science Convergence Equilibrium Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Real Functions Regularization methods Studies |
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| Title | An extragradient algorithm for solving bilevel pseudomonotone variational inequalities |
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