Weak and strong convergence of inertial Tseng's extragradient algorithms for solving variational inequality problems

References

• Takahahsi W, Yao JC. The split common fixed point problem for two finite families of nonlinear mappings in Hilbert spaces. J Nonlinear Convex Anal. 2019;20:173–195.
   Web of Science ®Google Scholar
• Dehaish BAB. Weak and strong convergence of algorithms for the sum of two accretive operators with applications. J Nonlinear Convex Anal. 2015;16:1321–1336.
   Web of Science ®Google Scholar
• Cho SY, Kang SM. Approximation of common solutions of variational inequalities via strict pseudocontractions. Acta Math Sci. 2012;32:1607–1618. doi: 10.1016/S0252-9602(12)60127-1
   Web of Science ®Google Scholar
• Qin X, Yao JC. Projection splitting algorithms for nonself operators. J Nonlinear Convex Anal. 2017;18:925–935.
   Web of Science ®Google Scholar
• Qin X, An NT. Smoothing algorithms for computing the projection onto a Minkowski sum of convex sets. Comput Optim Appl. 2019. DOI: 10.1007/s10589-019-00124-7
   Google Scholar
• Zhao X, Ng KF, Li C, et al. Linear regularity and linear convergence of projection-based methods for solving convex feasibility problems. Appl Math Optim. 2018;78:613–641. doi: 10.1007/s00245-017-9417-1
   Web of Science ®Google Scholar
• Censor Y, Gibali A, Reich S. The subgradient extragradientmethod for solving variational inequalities in Hilbert space. J Optim Theory Appl. 2011;148:318–335. doi: 10.1007/s10957-010-9757-3
   PubMed Web of Science ®Google Scholar
• Censor Y, Gibali A, Reich S. Algorithms for the split variational inequality problem. Numer Algo. 2012;59:301–323. doi: 10.1007/s11075-011-9490-5
   Web of Science ®Google Scholar
• Censor Y, Gibali A, Reich S. Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space. Optim Meth Softw. 2011;26:827–845. doi: 10.1080/10556788.2010.551536
   Web of Science ®Google Scholar
• Moudafi A, Xu HK. A DC regularization of split minimization problems. Appl Anal Optim. 2018;2:285–297.
   Google Scholar
• Cho SY. Strong convergence analysis of a hybrid algorithm for nonlinear operators in a Banach space. J Appl Anal Comput. 2018;8:19–31.
   Google Scholar
• Cho SY, Li W, Kang SM. Convergence analysis of an iterative algorithm for monotone operators. J Inequal Appl. 2013;2013. Article ID 199.
   Web of Science ®Google Scholar
• Malitsky YV. Projected reflected gradient methods for monotone variational inequalities. SIAM J Optim. 2015;25:502–520. doi: 10.1137/14097238X
   Web of Science ®Google Scholar
• Korpelevich GM. The extragradient method for finding saddle points and other problems. Ekonomikai Matematicheskie Metody. 1976;12:747–756.
   Google Scholar
• Thong DV, Hieu DV. Weak and strong convergence theorems for variational inequality problems. Numer Algor. 2018;78:1045–1060. doi: 10.1007/s11075-017-0412-z
   Web of Science ®Google Scholar
• Alvarez F. Weak convergence of a relaxed and inertial hybrid projection-proximal point algorithm for maximal monotone operators in Hilbert space. SIAM J Optim. 2004;14:773–782. doi: 10.1137/S1052623403427859
   Web of Science ®Google Scholar
• Alvarez F, Attouch H. An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set-Valued Anal. 2001;9:3–11. doi: 10.1023/A:1011253113155
   Google Scholar
• Polyak BT. Some methods of speeding up the convergence of iterative methods. Zh Vychisl Mat Mat Fiz. 1964;4:1–17.
   Google Scholar
• Thong DV, Hieu DV. An inertial method for solving split common fixed point problems. J Fixed Point Theory Appl. 2017;19:3029–3051. doi: 10.1007/s11784-017-0464-7
   Web of Science ®Google Scholar
• Thong DV, Vinh NT, Cho YJ. A strong convergence theorem for Tseng's extragradient method for solving variational inequality problems. Optim Lett. 2019. doi:10.1007/s11590-019-01391-3
   Google Scholar
• Shehu Y, Iyiola OS. Iterative algorithms for solving fixed point problems and variational inequalities with uniformly continuous monotone operators. Numer Algo. 2018;79:529–553. doi: 10.1007/s11075-017-0449-z
   Web of Science ®Google Scholar
• Attouch H, Peypouquet J, Redont P. A dynamical approach to an inertial forward-backward algorithm for convex minimization. SIAM J Optim. 2014;24:232–256. doi: 10.1137/130910294
   Web of Science ®Google Scholar
• Ochs P, Brox T, Pock T. Inertial proximal algorithm for strongly convex optimization. J Math Imaging Vision. 2015;53:171–181. doi: 10.1007/s10851-015-0565-0
   Web of Science ®Google Scholar
• Thong DV, Hieu DV. Modified Tseng's extragradient algorithms for variational inequality problems. J Fixed Point Appl. 2018;20. Article ID 152.
   Web of Science ®Google Scholar
• Yao YH, Yao JC. On modified iterative method for nonexpansive mappings and monotone mappings. Appl Math Comput. 2007;186:1551–1558.
   Web of Science ®Google Scholar
• Alvarez F, Attouch H. An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set-Valued Anal. 2001;9:3–11. doi: 10.1023/A:1011253113155
   Google Scholar
• Saejung S, Yotkaew P. Approximation of zeros of inverse strongly monotone operators in Banach spaces. Nonlinear Anal. 2012;75:742–750. doi: 10.1016/j.na.2011.09.005
   Web of Science ®Google Scholar
• Ofoedu EU. Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in a real Banach space. J Math Anal Appl. 2006;321:722–728. doi: 10.1016/j.jmaa.2005.08.076
   Web of Science ®Google Scholar
• Kraikaew R, Saejung S. Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Hilbert spaces. J Optim Theory Appl. 2014;163:399–412. doi: 10.1007/s10957-013-0494-2
   Web of Science ®Google Scholar