Open Access
Issue
RAIRO-Oper. Res.
Volume 55, Number 4, July-August 2021
Page(s) 2165 - 2180
DOI https://doi.org/10.1051/ro/2021091
Published online 08 July 2021
  • R.P. Agarwal, D. O’Regan and D.R. Sahu, Fixed Point Theory for Lipschitzian-Type Mappings with Applications, Topological Fixed Point Theory and Its Applications. Springer, New York, NY, USA (2009). [Google Scholar]
  • F. Alvarez, Weak convergence of a relaxed and inertial hybrid projection-proximal point algorithm for maximal monotone operators in Hilbert space. SIAM J. Optim. 14 (2004) 773–782. [Google Scholar]
  • H.H. Bauschke and P.L. Combttes, Convex Analysis and Monotone Operator Theory in Hilbert Space. Springer, Berlin (2011). [Google Scholar]
  • R.I. Bot and E.R. Csetnek, An inertial Tsengs type proximal algorithm for nonsmooth and nonconvex optimization problems. J. Optim. Theory Appl. 171 (2015) 600–616. [Google Scholar]
  • R.I. Bot, E.R. Csetnek and P.T. Vuong, The Forward-Backward-Forward Method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces. Preprint arXiv:1808.08084 (2018). [Google Scholar]
  • X. Cai, G. Gu and B. He, On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators. Comput. Optim. Appl. 57 (2014) 339–363. [Google Scholar]
  • S.Y. Cho, X. Qin, J.C. Yao and Y. Yao, Viscosity approximation splitting methods for monotone and nonexpansive operators in Hilbert spaces. J. Nonlinear Convex Anal. 19 (2018) 251–264. [Google Scholar]
  • A. Dixit, D.R. Sahu, A.K. Singh and T. Som, Application of a new accelerated algorithm to regression problems. Soft Comput. 24 (2020) 1539–1552. [Google Scholar]
  • A. Gibali, S. Reich and R. Zalas, Iterative methods for solving variational inequalities in Euclidean space. J. Fixed Point Theory Appl. 17 (2015) 775–811. [Google Scholar]
  • A.A. Goldstein, Convex programming in Hilbert spaces. Bull. Am. Math. Soc. 70 (1964) 709–710. [Google Scholar]
  • D.V. Hieu and S. Reich, Two Bregman projection methods for solving variational inequalities. Optimization (2020) 1–26. DOI: 10.1080/02331934.2020.1836634. [Google Scholar]
  • D.V. Hieu and D.V. Thong, New extragradient-like algorithms for strongly pseudomonotone variational inequalities. J. Global Optim. 70 (2018) 385–399. [Google Scholar]
  • D.V. Hieu, Y.J. Cho, Y.B. Xiao and P. Kumam, Modified extragradient method for pseudomonotone variational inequalities in infinite dimensional Hilbert spaces. Vietnam J. Math. (2020) 1–19. DOI: 10.1007/s10013-020-00447-7. [Google Scholar]
  • D.V. Hieu, J.J. Strodiot and L.D. Muu, An explicit extragradient algorithm for solving variational inequalities. J. Optim. Theory App. 185 (2020) 476–503. [Google Scholar]
  • D.V. Hieu, Y.J. Cho and Y.B. Xiao, Modified accelerated algorithms for solving variational inequalities. Int. J. Comput. Math. 97 (2020) 2233–2258. [Google Scholar]
  • D.V. Hieu, Y.J. Cho, Y.B. Xiao and P. Kumam, Relaxed extragradient algorithm for solving pseudomonotone variational inequalities in Hilbert spaces. Optimization 69 (2020) 2279–2304. [Google Scholar]
  • P.D. Khanh, A new extragradient method for strongly pseudomonotone variational inequalities. Numer. Funct. Anal. Optim. 37 (2016) 1131–1143. [Google Scholar]
  • P.D. Khanh and P.T. Vuong, Modified projection method for strongly pseudomonotone variational inequalities. J. Global Optim. 58 (2014) 341–350. [Google Scholar]
  • D.S. Kim, P.T. Vuong and P.D. Khanh, Qualitative properties of strongly pseudomonotone variational inequalities. Optim. Lett. 10 (2016) 1669–1679. [Google Scholar]
  • G.M. Korpelevich, The extragradient method for finding saddle points and other problems. Matecon 12 (1976) 747–756. [Google Scholar]
  • P.E. Mainge and M.L. Gobinddass, Convergence of one-step projected gradient methods for variational inequalities. J. Optim. Theory Appl. 171 (2016) 146–168. [Google Scholar]
  • Y.U. Malitsky and V.V. Semenov, A hybrid method without extrapolation step for solving variational inequality problems. J. Global Optim. 61 (2015) 193–202. [Google Scholar]
  • B.T. Polyak, Some methods of speeding up the convergence of iterarive methods. Zh. Vychisl. Mat. Mat. Fiz. 4 (1964) 1–17. [Google Scholar]
  • D.R. Sahu, Applications of the S-iteration process to constrained minimization problems and split feasibility problems. Fixed Point Theory Appl. 12 (2011) 187–204. [Google Scholar]
  • D.R. Sahu, Applications of accelerated computational methods for quasi-nonexpansive operators to optimization problems. Soft Comput. 24 (2020) 17887–17911. [Google Scholar]
  • D.R. Sahu, A. Pitea and M. Verma, A new iteration technique for nonlinear operators as concerns convex programming and feasibility problems. Numer. Algorithms 83 (2020) 421–449. [Google Scholar]
  • D.R. Sahu, J.C. Yao, M. Verma and K.K. Shukla, Convergence rate analysis of proximal gradient methods with applications to composite minimization problems. Optimization 70 (2021) 75–100. [Google Scholar]
  • M.V. Solodov and B.F. Svaiter, A new projection method for variational inequality problems. SIAM J. Control Optim. 37 (1999) 765–776. [Google Scholar]
  • G. Stampacchia, Forms bilineaires coercitives sur les ensembles convexes. C. R. Acad. Sci. Paris 258 (1964) 4413–4416. [Google Scholar]
  • B.S. Thakur and M. Postolache, Existence and approximation of solutions for generalized extended nonlinear variational inequalities. J. Inequal. Appl. 2013 (2013) 590. [Google Scholar]
  • D.V. Thong and D.V. Hieu, An inertial method for solving split common fixed point problems. J. Fixed Point Theory Appl. 19 (2017) 3029–3051. [Google Scholar]
  • D.V. Thong and D.V. Hieu, Weak and strong convergence theorems for variational inequality problems. Numer. Algorithms 78 (2017) 1045–1060. [Google Scholar]
  • D.V. Thong and D.V. Hieu, New extragradient methods for solving variational inequality problems and fixed point problems. J. Fixed Point Theory Appl. 20 (2018) 129. [Google Scholar]
  • D.V. Thong and D.V. Hieu, Inertial extragradient algorithms for strongly pseudomonotone variational inequalities. J. Comput. Appl. Math. 341 (2018) 80–98. [Google Scholar]
  • D.V. Thong and P.T. Vuong, Modified Tseng’s extragradient methods for solving pseudomonotone variational inequalities. Optimization 68 (2019) 2203–2222. [Google Scholar]
  • P. Tseng, A modified forward-backward splitting method for maximal monotone mappings. SIAM J. Control Optim. 38 (2000) 431–446. [Google Scholar]
  • M. Verma and K.K. Shukla, Convergence analysis of accelerated proximal extra-gradient method with applications. Neurocomputing 388 (2020) 288–300. [Google Scholar]
  • F.H. Wang and H.K. Xu, Weak and strong convergence theorems for variational inequality and fixed point problems with Tseng’s extragradient method. Taiwan. J. Math. 16 (2012) 1125–1136. [Google Scholar]
  • Y. Yao, R. Chen and H.K. Xu, Schemes for finding minimum-norm solutions of variational inequalities. Nonlinear Anal. 72 (2010) 3447–3456. [Google Scholar]
  • Y. Yao, M. Postolache, Y.C. Liou and J.C. Yao, Construction algorithms for a class of monotone variational inequalities. Optim. Lett. 10 (2016) 1519–1528. [Google Scholar]
  • Y. Yao, M. Postolache and J.C. Yao, An iterative algorithm for solving generalized variational inequalities and fixed points problems. Mathematics 7 (2019) 61. [Google Scholar]
  • Y. Yao, M. Postolache and J.C. Yao, Iterative algorithms for generalized variational inequalities. UPB Sci. Bull., Ser. A 81 (2019) 3–16. [Google Scholar]
  • Y. Yao, M. Postolache and J.C. Yao, Strong convergence of an extragradient algorithm for variational inequality and fixed point problems. U. Politeh. Buch. Ser. A 82 (2020) 3–12. [Google Scholar]
  • X.P. Zhao, D.R. Sahu and C.F. Wen, Iterative methods for system of variational inclusions involving accretive operators and applications. Fixed Point Theory 19 (2018) 801–822. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.