Modified subgradient extragradient algorithms for variational inequality problems and fixed point problems

References

• Korpelevich GM. The extragradient method for finding saddle points and other problems. Ekonomikai Matematicheskie Metody. 1976;12:747–756.
   Google Scholar
• Censor Y, Gibali A, Reich S. Algorithms for the split variational inequality problem. Numer Algorithms. 2012;59:301–323.
   Web of Science ®Google Scholar
• Censor Y, Gibali A, Reich S. The subgradient extragradient method for solving variational inequalities in Hilbert space. J Optim Theory Appl. 2011;148:318–335.
   PubMed 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.
   Web of Science ®Google Scholar
• Censor Y, Gibali A, Reich S. Extensions of Korpelevich’s extragradient method for the variational inequality problem in Euclidean space. Optimization. 2012;61:1119–1132.
   Web of Science ®Google Scholar
• Ceng LC, Hadjisavvas N, Wong NC. Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems. J Glob Optim. 2010;46:635–646.
   Web of Science ®Google Scholar
• Hieu DV, Anh PK, Muu LD. Modified hybrid projection methods for finding common solutions to variational inequality problems. Comput Optim Appl. 2017;66:75–96.
   Web of Science ®Google Scholar
• Hieu DV. Halpern subgradient extragradient method extended to equilibrium problems. Rev R Acad Cienc Exactas Fs Nat Ser A Math RACSAM. 2017;111:823–840.
   Web of Science ®Google Scholar
• Hieu DV, Muu LD, Anh PK. Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings. Numer Algorithms. 2016;73:197–217.
   Web of Science ®Google Scholar
• Hieu DV. Parallel extragradient-proximal methods for split equilibrium problems. Math Model Anal. 2016;21:478–501.
   Web of Science ®Google Scholar
• Hieu DV. An explicit parallel algorithm for variational inequalities. Bull Malays Math Sci Soc. 2017. DOI:10.1007/s40840-017-0474-z
   Web of Science ®Google Scholar
• Hieu DV, Thong DV. New extragradient-like algorithms for strongly pseudomonotone variational inequalities. J Glob Optim. 2017. DOI:10.1007/s10898-017-0564-3
   Web of Science ®Google Scholar
• Malitsky YV, Semenov VV. A hybrid method without extrapolation step for solving variational inequality problems. J Glob Optim. 2015;61:193–202.
   Web of Science ®Google Scholar
• Malitsky YV. Projected reflected gradient methods for monotone variational inequalities. SIAM J Optim. 2015;25:502–520.
   Web of Science ®Google Scholar
• Nadezhkina N, Takahashi W. Strong convergence theorem by a hybrid method for nonexpansive mappings and Lipschitz-continuous monotone mappings. SIAM J Optim. 2006;16:1230–1241.
   Web of Science ®Google Scholar
• Solodov MV, Svaiter BF. A new projection method for variational inequality problems. SIAM J Control Optim. 1999;37:765–776.
   Web of Science ®Google Scholar
• Tseng P. A modified forward-backward splitting method for maximal monotone mappings. SIAM J Control Optim. 2000;38:431–446.
   Web of Science ®Google Scholar
• Thong DV, Hieu DV. Weak and strong convergence theorems for variational inequality problems. Numer Algorithms. 2017. DOI:10.1007/s11075-017-0412-z
   Web of Science ®Google Scholar
• Yao Y, Marino G, Muglia L. A modified Korpelevich’s method convergent to the minimum-norm solution of a variational inequality. Optimization. 2014;63:559–569.
   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.
   Web of Science ®Google Scholar
• Iiduka H. Acceleration method for convex optimization over the fixed point set of a nonexpansive mapping. Math Program Ser A. 2015;149:131–165.
   Web of Science ®Google Scholar
• Maingé PE. A hybrid extragradient-viscosity method for monotone operators and fixed point problems. SIAM J Control Optim. 2008;47:1499–1515.
   Web of Science ®Google Scholar
• Li M, Yao Y. Strong convergence of an iterative algorithm for λ-strictly pseudo-contractive mappings in Hilbert spaces. An St Univ Ovidius Constanta. 2010;18:219–228.
   Google Scholar
• Shehu Y, Cholamjiak P. Another look at the split common fixed point problem for demicontractive operators. Rev R Acad Cienc Exactas Fs Nat Ser A Math RACSAM. 2016;110:201–218.
   Web of Science ®Google Scholar
• Ceng LC, Anasri QH, Yao JC. Mann type iterative methods for finding a common solution of split feasibility and fixed point problems. Positivity. 2012;16:471–495.
   Web of Science ®Google Scholar
• Dang Y, Gao Y. The strong convergence of a KM-CQ-like algorithm for a split feasibility problem. Inverse Probl. 2011;27:015007.
   Web of Science ®Google Scholar
• Mann WR. Mean value methods in iteration. Proc Amer Math Soc. 1953;4:506–510.
   Web of Science ®Google Scholar
• Chidume CE, Maruster S. Iterative methods for the computation of fixed points of demicontractive mappings. J Comput Appl Math. 2010;234:861–882.
   Web of Science ®Google Scholar
• Boonchari D, Saejung S. Construction of common fixed points of a countable family of λ-demicontractive mappings in arbitrary Banach spaces. Appl Math Comput. 2010;216:173–178.
   Web of Science ®Google Scholar
• Thong DV. Viscosity approximation methods for solving fixed point problems and split common fixed point problems. J Fixed Point Theory Appl. 2017;19:1481–1499.
   Web of Science ®Google Scholar
• Thong DV, Hieu DV. An inertial method for solving split common fixed point problems. J Fixed Point Theory Appl. 2017. DOI:10.1007/s11784-017-0464-7
   Web of Science ®Google Scholar
• Hicks TL, Kubicek JD. On the Mann iteration process in a Hilbert space. J Math Anal Appl. 1997;59:498–504.
   Web of Science ®Google Scholar
• Mongkolkeha C, Cho YJ, Kumam P. Convergence theorems for k-dimeicontactive mappings in Hilbert spaces. Math Inequal Appl. 2013;16:1065–1082.
   Web of Science ®Google Scholar
• Reich S. Constructive techniques for accretive and monotone operators. Applied nonlinear analysis. New York (NY): Academic Press; 1979. p. 335–345.
   Google Scholar
• Xu HK. Iterative algorithms for nonlinear operators. J Lond Math Soc. 2002;66:240–256.
   Web of Science ®Google Scholar
• Yamada I, Ogura N. Hybrid steepest descent method for variational inequality operators over the problem certain fixed point set of quasi-nonexpansive mappings. Numer Funct Anal Optim. 2004;25:619–655.
   Web of Science ®Google Scholar