Strong convergence result for solving monotone variational inequalities in Hilbert space
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In this paper, we study strong convergence of the algorithm for solving classical variational inequalities problem with Lipschitz-continuous and monotone mapping in real Hilbert space. The algorithm is inspired by Tseng’s extragradient method and the viscosity method with a simple step size. A strong convergence theorem for our algorithm is proved without any requirement of additional projections and the knowledge of the Lipschitz constant of the mapping. Finally, we provide some numerical experiments to show the efficiency and advantage of the proposed algorithm.
KeywordsVariational inequalities Projection Extragradient method Monotone mapping Convex set
Mathematics Subject Classification (2010)47J20 90C25 90C30 90C52
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The authors would like to thank the Associate Editor and the anonymous referees for their valuable comments and suggestions which helped to improve the original version of this paper.
The Project was supported by the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2017JM1014).
- 11.Duong, V.T., Dang V.H.: Weak and strong convergence theorems for variational inequality problems. Numer Algor, https://doi.org/10.1007/s11075-017-0412-z
- 17.Antipin, A.S.: On a method for convex programs using a symmetrical modification of the Lagrange function. Ekonomika i Matematicheskie Metody. 12(6), 1164–1173 (1976)Google Scholar