Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces

By Rapeepan Kraikaew, Satit Saejung. Journal of Optimization Theory and Applications, 2014

308 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1fac7e459275365c6a29e6d662199310550d72f5

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In Civil and Structural Engineering

1. Yekini Shehu
2. Oluwatosin Temitope Mewomo
3. Duong Viet Thong
4. Timilehin Opeyemi Alakoya
5. Dang Van Hieu
6. Olaniyi Samuel Iyiola
7. Lateef Olakunle Jolaoso
8. Lu-Chuan Ceng

In Computational Theory and Mathematics

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2. Yekini Shehu
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4. Lateef Olakunle Jolaoso
5. Timilehin Opeyemi Alakoya
6. Dang Van Hieu
7. Adeolu Taiwo
8. Olaniyi Samuel Iyiola

In Numerical Analysis

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Citations in the corpus

• Hybrid inertial subgradient extragradient methods for variational inequalities and fixed point problems involving asymptotically nonexpansive mappings (2019, methodology): “the VIP in [22] is extended to develop our modified inertial subgradient extragradient method with line-search process for solving the VIP and CFPP, which is based on inertial subgradient extragradient method with line-search process, hybrid steepest-descent method, and viscosity approximation metho”
• Modified subgradient extragradient algorithms for solving monotone variational inequalities (2018, methodology): “Rapeepan and Satit [16] used the subgradient extragraduent method and Halpern method to propose an algorithm for solving VI(C, F).”
• An efficient iterative method for finding common fixed point and variational inequalities in Hilbert spaces (2018, methodology): “The algorithm structure requires only one projection onto the feasible set C of the VI (1) unlike the results in [28,33,40].”
• Single projection method for pseudo-monotone variational inequality in Hilbert spaces (2018, background): “[12,14,18,19]) where the operator is assumed to be monotone.”
• Modified subgradient extragradient algorithms for variational inequality problems and fixed point problems (2018, methodology): “11 [20]: Let A : H → H be a monotone and L-Lipschitz continuous mapping on H.”
• A self adaptive inertial subgradient extragradient algorithm for variational inequality and common fixed point of multivalued mappings in Hilbert spaces (2019, background): “We highlight some further contributions made in this paper as follows: (i) Unlike the results of Censor et al. [13], KraikaewandSaejung [50], Thong andHieu [27]which require that the stepsize satisfies µn = µ ∈ (︂ 0, 1L )︂ , where L is the Lipschitz constant of A.”
• Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence (2020, methodology): “(c) Algorithm 1 requires, at each iteration, only one projection onto the feasible set C and it is different from other methods in [8, 9, 10, 11, 13, 29, 45] where more than one projection per iteration is needed.”
• Strong convergence of a double projection-type method for monotone variational inequalities in Hilbert spaces (2018, methodology): “Under the same assumptions, Kraikaew and Saejung [27] obtained a strong convergence result using a combination of a Halpern-type iterative scheme and the subgradient extragradient method.”