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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 65, 2016 - Issue 10
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Articles

A splitting algorithm for a class of bilevel equilibrium problems involving nonexpansive mappings

Phung M. DucBasic Department, Technical Vocational College of Medical Equipment, Hanoi, Vietnam.View further author information
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Le D. MuuOptimization and Control Department, Institute of Mathematics, VAST, Hanoi, Vietnam.Correspondence[email protected]
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Pages 1855-1866 | Received 09 Nov 2015, Accepted 24 May 2016, Published online: 16 Jun 2016

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Le Hai Yen & Le Dung Muu. (2022) A parallel subgradient projection algorithm for quasiconvex equilibrium problems under the intersection of convex sets. Optimization 71:15, pages 4447-4462.
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Pham Ngoc Anh & Le Thi Hoai An. (2019) New subgradient extragradient methods for solving monotone bilevel equilibrium problems. Optimization 68:11, pages 2099-2124.
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Articles from other publishers (16)

Zai-Yun Peng, Dan Li, Yong Zhao & Ren-Li Liang. (2023) An accelerated subgradient extragradient algorithm for solving bilevel variational inequality problems involving non-Lipschitz operator. Communications in Nonlinear Science and Numerical Simulation 127, pages 107549.
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Lateef Olakunle Jolaoso, Kazeem Olalekan Aremu & Olawale Kazeem Oyewole. (2022) A self-adaptive inertial subgradient extragradient algorithm for solving bilevel equilibrium problems. Rendiconti del Circolo Matematico di Palermo Series 2.
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Pham Ngoc Anh. (2022) Hybrid Inertial Contraction Algorithms for Solving Variational Inequalities with Fixed Point Constraints in Hilbert Spaces. Acta Mathematica Vietnamica 47:4, pages 743-753.
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Porntip Promsinchai & Nimit Nimana. (2022) A Subgradient-Type Extrapolation Cyclic Method for Solving an Equilibrium Problem over the Common Fixed-Point Sets. Symmetry 14:5, pages 992.
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Le Dung Muu & Xuan Thanh Le. (2021) On fixed point approach to equilibrium problem. Journal of Fixed Point Theory and Applications 23:4.
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Dang Van Hieu & Abdellatif Moudafi. (2020) Regularization projection method for solving bilevel variational inequality problem. Optimization Letters 15:1, pages 205-229.
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Yusuf I. Suleiman, Habib ur Rehman, Aviv Gibali & Poom Kumam. (2020) A self-adaptive extragradient–CQ method for a class of bilevel split equilibrium problem with application to Nash Cournot oligopolistic electricity market models. Computational and Applied Mathematics 39:4.
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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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Stephan Dempe. 2020. Bilevel Optimization. Bilevel Optimization 581 672 .
Nguyen The Vinh & Le Dung Muu. (2019) Inertial Extragradient Algorithms for Solving Equilibrium Problems. Acta Mathematica Vietnamica 44:3, pages 639-663.
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Pham Ky Anh & Trinh Ngoc Hai. (2018) Novel self-adaptive algorithms for non-Lipschitz equilibrium problems with applications. Journal of Global Optimization 73:3, pages 637-657.
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L. Q. Anh & N. V. Hung. (2018) Levitin–Polyak well-posedness for strong bilevel vector equilibrium problems and applications to traffic network problems with equilibrium constraints. Positivity 22:5, pages 1223-1239.
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Le Dung Muu & Xuan Thanh Le. (2018) A splitting algorithm for finding fixed points of nonexpansive mappings and solving equilibrium problems. Journal of Fixed Point Theory and Applications 20:3.
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Pham Ky Anh & Trinh Ngoc Hai. (2018) A splitting algorithm for equilibrium problem given by the difference of two bifunctions. Journal of Fixed Point Theory and Applications 20:1.
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Le Quang Thuy & Trinh Ngoc Hai. (2017) A Projected Subgradient Algorithm for Bilevel Equilibrium Problems and Applications. Journal of Optimization Theory and Applications 175:2, pages 411-431.
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Xiaolong Qin & Jen-Chih Yao. (2016) Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators. Journal of Inequalities and Applications 2016:1.
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