An Explicit Parallel Algorithm for Variational Inequalities

Hieu, Dang Van

doi:10.1007/s40840-017-0474-z

Cited by 16 publications

(1 citation statement)

References 23 publications

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“…provided that VI(C, A) is non-empty. In recent years, the extragradient method has received great attention by many authors, who improved it in various ways, see, e.g., Censor et al (2011aCensor et al ( , b, c, 2012, Hieu et al (2016Hieu et al ( , 2017, Hieu (2016Hieu ( , 2017, Hieu and Thong (2018a, b), Malitsky and Semenov (2015), Malitsky (2015), Solodov and Svaiter (1999), Thong and Hieu (2018a, b, c, e), Yao et al (2014), and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Strong convergence of extragradient methods with a new step size for solving variational inequality problems

Thong

Hieu

2019

Comp. Appl. Math.

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In this paper, we propose two different kinds of extragradient methods with a new step size for finding an element of the set of solutions of the variational inequality problem for a monotone and Lipschitz continuous operator in real Hilbert spaces. We only use one projection to design the algorithms and the strong convergence theorems proved without the prior knowledge of the Lipschitz constant of cost operator. Numerical experiments illustrate the performances of our new algorithms and provide a comparison with related algorithms. Keywords Extragradient method • Subgradient extragradient method • Tseng's extragradient method • Mann-type method • Variational inequality problem Mathematics Subject Classification 65Y05 • 65K15 • 68W10 • 47H09 • 47J25 Communicated by Gabriel Haeser. Dedicated to Professor Pham Ky Anh on the Occasion of his 70th Birthday.

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