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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 58, 2009 - Issue 8
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Original Articles

Bilevel convex programming models

R. Trujillo-Cortez Sociedad Hipotecaria Federal, México Distrito Federal, MéxicoCorrespondence[email protected]
&
S. Zlobec Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada
Pages 1009-1028 | Received 23 Jun 2006, Accepted 23 Jul 2007, Published online: 02 Nov 2009

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Duong Viet Thong, Xiao-Huan Li, Qiao-Li Dong, Yeol Je Cho & Themistocles M. Rassias. (2022) A projection and contraction method with adaptive step sizes for solving bilevel pseudo-monotone variational inequality problems. Optimization 71:7, pages 2073-2096.
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Pham Van Huy, Le Huynh My Van, Nguyen Duc Hien & Tran Viet Anh. (2022) Modified Tseng's extragradient methods with self-adaptive step size for solving bilevel split variational inequality problems. Optimization 71:6, pages 1721-1748.
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Duong Viet Thong & Dang Van Hieu. (2020) A strong convergence of modified subgradient extragradient method for solving bilevel pseudomonotone variational inequality problems. Optimization 69:6, pages 1313-1334.
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Jong Kyu Kim, Pham N. Anh & Trinh N. Hai. (2017) The Bruck's ergodic iteration method for the Ky Fan inequality over the fixed point set. International Journal of Computer Mathematics 94:12, pages 2466-2480.
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Articles from other publishers (13)

Tran Van Thang. (2024) Proximal Subgradient Algorithm for a Class of Nonconvex Bilevel Equilibrium Problems. Bulletin of the Malaysian Mathematical Sciences Society 47:2.
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J. A. Abuchu, G. C. Ugwunnadi & O. K. Narain. (2023) An inertial projection and contraction method for solving bilevel quasimonotone variational inequality problems. The Journal of Analysis 31:4, pages 2915-2942.
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Francis Akutsah, Akindele Adebayo Mebawondu, Godwin Chidi Ugwunnadi, Paranjothi Pillay & Ojen Kumar Narain. (2022) Inertial extrapolation method with regularization for solving a new class of bilevel problem in real Hilbert spaces. SeMA Journal 80:3, pages 503-524.
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Ferdinard U. Ogbuisi, Yekini Shehu & Jen-Chih Yao. (2023) Relaxed Single Projection Methods for Solving Bilevel Variational Inequality Problems in Hilbert Spaces. Networks and Spatial Economics 23:3, pages 641-678.
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Yanlai Song & Omar Bazighifan. (2022) Regularization Method for the Variational Inequality Problem over the Set of Solutions to the Generalized Equilibrium Problem. Mathematics 10:14, pages 2443.
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Jun Yang. (2022) Projection and Contraction Methods for Solving Bilevel Pseudomonotone Variational Inequalities. Acta Applicandae Mathematicae 177:1.
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Pham Ngoc Anh & Ho Phi Tu. (2020) Subgradient projection methods extended to monotone bilevel equilibrium problems in Hilbert spaces. Numerical Algorithms 86:1, pages 55-74.
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Pham Ngoc Anh & Le Thi Hoai An. (2019) Modified parallel projection methods for the multivalued lexicographic variational inequalities using proximal operator in Hilbert spaces. Mathematical Methods in the Applied Sciences 43:6, pages 3260-3279.
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Duong Viet Thong, Nguyen Anh Triet, Xiao-Huan Li & Qiao-Li Dong. (2019) Strong convergence of extragradient methods for solving bilevel pseudo-monotone variational inequality problems. Numerical Algorithms 83:3, pages 1123-1143.
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Stephan Dempe. 2020. Bilevel Optimization. Bilevel Optimization 581 672 .
Pham N. Anh, Le Q. Thuy & Tran T. H. Anh. (2017) Strong Convergence Theorem for the Lexicographic Ky Fan Inequality. Vietnam Journal of Mathematics 46:3, pages 517-530.
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Pham Ngoc Anh, Tran T. H. Anh & Takahito Kuno. (2017) Convergence Theorems for Variational Inequalities on the Solution Set of Ky Fan Inequalities. Acta Mathematica Vietnamica 42:4, pages 761-773.
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Tran TH Anh, Le B Long & Tran V Anh. (2014) A projection method for bilevel variational inequalities. Journal of Inequalities and Applications 2014:1.
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