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Numerical Functional Analysis and Optimization Volume 36, 2015 - Issue 8
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Original Articles

A Hybrid Proximal-Extragradient Algorithm with Inertial Effects

Radu Ioan Boţ Faculty of Mathematics, University of Vienna, Vienna, AustriaCorrespondence[email protected]
&
Ernö Robert Csetnek Faculty of Mathematics, University of Vienna, Vienna, Austria
Pages 951-963 | Received 24 Feb 2015, Accepted 14 Apr 2015, Published online: 27 Jul 2015

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Zhongbing Xie, Gang Cai & Bing Tan. (2024) Inertial subgradient extragradient method for solving pseudomonotone equilibrium problems and fixed point problems in Hilbert spaces. Optimization 73:5, pages 1329-1354.
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Alfredo N. Iusem & R. T. Marcavillaca. (2023) On Proximal Algorithms with Inertial Effects Beyond Monotonicity. Numerical Functional Analysis and Optimization 44:15-16, pages 1583-1601.
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L. O. Jolaoso, T. O. Alakoya, A. Taiwo & O. T. Mewomo. (2021) Inertial extragradient method via viscosity approximation approach for solving equilibrium problem in Hilbert space. Optimization 70:2, pages 387-412.
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M. Marques Alves & Samara Costa Lima. (2020) On the convergence rate of the scaled proximal decomposition on the graph of a maximal monotone operator (SPDG) algorithm. Optimization 69:11, pages 2371-2381.
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Duong Viet Thong & Dang Van Hieu. (2020) Mann-type algorithms for variational inequality problems and fixed point problems. Optimization 69:10, pages 2305-2326.
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Yu Cao & Ke Guo. (2020) On the convergence of inertial two-subgradient extragradient method for variational inequality problems. Optimization 69:6, pages 1237-1253.
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Duong Viet Thong & Nguyen The Vinh. (2019) Inertial methods for fixed point problems and zero point problems of the sum of two monotone mappings. Optimization 68:5, pages 1037-1072.
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Radu Ioan Boţ & Ernö Robert Csetnek. (2017) Penalty schemes with inertial effects for monotone inclusion problems. Optimization 66:6, pages 965-982.
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Qiao-Li Dong, Yan-Yan Lu & Jinfeng Yang. (2016) The extragradient algorithm with inertial effects for solving the variational inequality. Optimization 65:12, pages 2217-2226.
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Mathieu Barré, Adrien B. Taylor & Francis Bach. (2022) Principled analyses and design of first-order methods with inexact proximal operators. Mathematical Programming 201:1-2, pages 185-230.
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Chibueze C. Okeke, Lateef O. Jolaoso & Yekini Shehu. (2023) Inertial accelerated algorithms for solving split feasibility with multiple output sets in Hilbert spaces. International Journal of Nonlinear Sciences and Numerical Simulation 24:2, pages 769-790.
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Yujiao Zeng, Gang Cai & Qiao Li Dong. (2022) Self Adaptive Iterative Algorithm for Solving Variational Inequality Problems and Fixed Point Problems in Hilbert Spaces. Acta Applicandae Mathematicae 183:1.
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Abdulkarim Hassan Ibrahim, Poom Kumam, Min Sun, Parin Chaipunya & Auwal Bala Abubakar. (2023) Projection method with inertial step for nonlinear equations: Application to signal recovery. Journal of Industrial and Management Optimization 19:1, pages 30.
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Chibueze C. Okeke. (2022) An improved inertial extragradient subgradient method for solving split variational inequality problems. Boletín de la Sociedad Matemática Mexicana 28:1.
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Abd-semii Oluwatosin-Enitan Owolabi, Timilehin Opeyemi Alakoya, Adeolu Taiwo & Oluwatosin Temitope Mewomo. (2022) A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings. Numerical Algebra, Control & Optimization 12:2, pages 255.
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Godwin Amechi Okeke, Mujahid Abbas, Manuel De la Sen & Hira Iqbal. (2021) Accelerated Modified Tseng’s Extragradient Method for Solving Variational Inequality Problems in Hilbert Spaces. Axioms 10:4, pages 248.
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Zhongbing Xie, Gang Cai, Xiaoxiao Li & Qiao-Li Dong. (2021) Strong Convergence of the Modified Inertial Extragradient Method with Line-Search Process for Solving Variational Inequality Problems in Hilbert Spaces. Journal of Scientific Computing 88:3.
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Godwin Ugwunnadi. (2021) Viscosity approximation method for solving variational inequality problem in real Banach spaces. Armenian Journal of Mathematics 13:3, pages 1-20.
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Duong Viet Thong, Vu Tien Dung & Yeol Je Cho. (2020) A new strong convergence for solving split variational inclusion problems. Numerical Algorithms 86:2, pages 565-591.
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Qiao-Li Dong, Shang-Hong Ke, Yeol Je Cho & Themistocles M. Rassias. 2021. Advances in Metric Fixed Point Theory and Applications. Advances in Metric Fixed Point Theory and Applications 61 83 .
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M. Marques Alves & Raul T. Marcavillaca. (2019) On Inexact Relative-Error Hybrid Proximal Extragradient, Forward-Backward and Tseng’s Modified Forward-Backward Methods with Inertial Effects. Set-Valued and Variational Analysis 28:2, pages 301-325.
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Godwin Amechi Okeke, Mujahid Abbas & Manuel de la Sen. (2020) Inertial Subgradient Extragradient Methods for Solving Variational Inequality Problems and Fixed Point Problems. Axioms 9:2, pages 51.
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Duong Viet Thong, Nguyen The Vinh & Yeol Je Cho. (2019) New strong convergence theorem of the inertial projection and contraction method for variational inequality problems. Numerical Algorithms 84:1, pages 285-305.
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Liya Liu & Xiaolong Qin. (2020) ON THE STRONG CONVERGENCE OF A PROJECTION-BASED ALGORITHM IN HILBERT SPACES. Journal of Applied Analysis & Computation 10:1, pages 104-117.
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Seifu Endris Yimer, Poom Kumam, Anteneh Getachew Gebrie & Rabian Wangkeeree. (2019) Inertial Method for Bilevel Variational Inequality Problems with Fixed Point and Minimizer Point Constraints. Mathematics 7:9, pages 841.
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M. Marques Alves & Marina Geremia. (2018) Iteration complexity of an inexact Douglas-Rachford method and of a Douglas-Rachford-Tseng’s F-B four-operator splitting method for solving monotone inclusions. Numerical Algorithms 82:1, pages 263-295.
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Duong Viet Thong & Dang Van Hieu. (2018) Inertial subgradient extragradient algorithms with line-search process for solving variational inequality problems and fixed point problems. Numerical Algorithms 80:4, pages 1283-1307.
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C. E. Chidume, M. O. Uba, M. I. Uzochukwu, E. E. Otubo & K. O. Idu. (2018) A Strong Convergence Theorem for an Iterative Method for Finding Zeros of Maximal Monotone Maps with Applications to Convex Minimization and Variational Inequality Problems. Proceedings of the Edinburgh Mathematical Society 62:1, pages 241-257.
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Yonghong Yao, Mihai Postolache & Jen-Chih Yao. (2019) An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems. Mathematics 7:1, pages 61.
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Duong Viet Thong & Dang Van Hieu. (2018) Modified Tseng’s extragradient algorithms for variational inequality problems. Journal of Fixed Point Theory and Applications 20:4.
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Lixin Zhang, Changjie Fang & Shenglan Chen. (2018) An inertial subgradient-type method for solving single-valued variational inequalities and fixed point problems. Numerical Algorithms 79:3, pages 941-956.
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Duong Viet Thong & Dang Van Hieu. (2018) Inertial extragradient algorithms for strongly pseudomonotone variational inequalities. Journal of Computational and Applied Mathematics 341, pages 80-98.
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Duong Viet Thong & Dang Van Hieu. (2017) Modified subgradient extragradient method for variational inequality problems. Numerical Algorithms 79:2, pages 597-610.
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Q. L. Dong, Y. J. Cho, L. L. Zhong & Th. M. Rassias. (2017) Inertial projection and contraction algorithms for variational inequalities. Journal of Global Optimization 70:3, pages 687-704.
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Radu Ioan Boţ, Ernö Robert Csetnek & Nimit Nimana. (2017) An Inertial Proximal-Gradient Penalization Scheme for Constrained Convex Optimization Problems. Vietnam Journal of Mathematics 46:1, pages 53-71.
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Radu Ioan Boţ, Ernö Robert Csetnek & Nimit Nimana. (2017) Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data. Optimization Letters 12:1, pages 17-33.
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Qiao-Li Dong, Yeol Je Cho & Themistocles M. Rassias. 2018. Applications of Nonlinear Analysis. Applications of Nonlinear Analysis 175 191 .
Q-L Dong, A Gibali, D Jiang & Y Tang. (2017) Bounded perturbation resilience of extragradient-type methods and their applications. Journal of Inequalities and Applications 2017:1.
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Duong Viet Thong & Dang Van Hieu. (2017) An inertial method for solving split common fixed point problems. Journal of Fixed Point Theory and Applications 19:4, pages 3029-3051.
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Maicon Marques Alves & Samara Costa Lima. (2017) An Inexact Spingarn’s Partial Inverse Method with Applications to Operator Splitting and Composite Optimization. Journal of Optimization Theory and Applications 175:3, pages 818-847.
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Radu Ioan Boţ, Ernö Robert Csetnek & Szilárd Csaba László. (2016) An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions. EURO Journal on Computational Optimization 4:1, pages 3-25.
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