Three novel inertial explicit Tseng's extragradient methods for solving pseudomonotone variational inequalities

References

• Konnov IV. On systems of variational inequalities. Russian Math Izv-Vyssh Uchebn Zaved Mat. 1997;41:77–86.
   Google Scholar
• Stampacchia G. Formes bilinéaires coercitives sur les ensembles convexes. C R Hebd Seances Acad Sci. 1964;258(18):4413.
   Google Scholar
• Elliott CM. Variational and quasivariational inequalities applications to free–boundary probLems. (claudio baiocchi and antónio capelo). SIAM Rev. 1987;29(2):314–315.
   Google Scholar
• Kassay G, Kolumbán J, Páles Z. On Nash stationary points. Publ Math. 1999;54(3–4):267–279.
   Google Scholar
• Kassay G, Kolumbán J, Páles Z. Factorization of minty and stampacchia variational inequality systems. Eur J Oper Res. 2002;143(2):377–389.
   Web of Science ®Google Scholar
• Konnov I. Equilibrium models and variational inequalities. Vol. 210. Amsterdam: Elsevier; 2007.
   Google Scholar
• Nagurney A. Network economics: a variational inequality approach. Boston: Academic; 1999.
   Google Scholar
• Takahashi W. Introduction to nonlinear and convex analysis. Yokohama: Yokohama Publishers; 2009.
   Google Scholar
• Ceng L, Petruşel A, Qin X, et al. A modified inertial subgradient extragradient method for solving pseudomonotone variational inequalities and common fixed point problems. Fixed Point Theory. 2020;21(1):93–108.
   Web of Science ®Google Scholar
• Ceng L-C, Petruşel A, Yao J-C. On mann viscosity subgradient extragradient algorithms for fixed point problems of finitely many strict pseudocontractions and variational inequalities. Mathematics. 2019;7(10):925.
   Web of Science ®Google Scholar
• Ceng L-C, Qin X, Shehu Y, et al. Mildly inertial subgradient extragradient method for variational inequalities involving an asymptotically nonexpansive and finitely many nonexpansive mappings. Mathematics. 2019c;7(10):881.
   Web of Science ®Google Scholar
• Ceng L-C, Yuan Q. Composite inertial subgradient extragradient methods for variational inequalities and fixed point problems. J Inequal Appl. 2019;2019(1):1–20.
   PubMed 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. 2010;148(2):318–335.
   Web of Science ®Google Scholar
• Censor Y, Gibali A, Reich S. Extensions of Korpelevich extragradient method for the variational inequality problem in Euclidean space. Optimization. 2012;61(9):1119–1132.
   Web of Science ®Google Scholar
• Iusem AN, Svaiter BF. A variant of Korpelevich's method for variational inequalities with a new search strategy. Optimization. 1997;42(4):309–321.
   Google Scholar
• Korpelevich G. The extragradient method for finding saddle points and other problems. Matecon. 1976;12:747–756.
   Google Scholar
• Moudafi A. Viscosity approximation methods for fixed-points problems. J Math Anal Appl. 2000;241(1):46–55.
   Web of Science ®Google Scholar
• Noor MA. Some iterative methods for nonconvex variational inequalities. Comput Math Model. 2010;21(1):97–108.
   Google Scholar
• Tseng P. A modified forward-backward splitting method for maximal monotone mappings. SIAM J Control Optim. 2000;38(2):431–446.
   Web of Science ®Google Scholar
• Yang J, Liu H. A modified projected gradient method for monotone variational inequalities. J Optim Theory Appl. 2018;179(1):197–211.
   Web of Science ®Google Scholar
• Yang J, Liu H, Liu Z. Modified subgradient extragradient algorithms for solving monotone variational inequalities. Optimization. 2018;67(12):2247–2258.
   Web of Science ®Google Scholar
• Zhang L, Fang C, Chen S. An inertial subgradient-type method for solving single-valued variational inequalities and fixed point problems. Numer Algorithms. 2018;79(3):941–956.
   Web of Science ®Google Scholar
• Ansari QH, Islam M, Yao J-C. Nonsmooth variational inequalities on Hadamard manifolds. Appl Anal. 2018;99(2):340–358.
   Web of Science ®Google Scholar
• Ceng L-C, Petruşel A, Wen C-F, et al. Inertial-like subgradient extragradient methods for variational inequalities and fixed points of asymptotically nonexpansive and strictly pseudocontractive mappings. Mathematics. 2019;7(9):860.
   Web of Science ®Google Scholar
• Ceng L-C, Shang M. Hybrid inertial subgradient extragradient methods for variational inequalities and fixed point problems involving asymptotically nonexpansive mappings. Optimization. 2019;70(4):715–740.
   Web of Science ®Google Scholar
• Ceng L-C, Shang M. Composite extragradient implicit rule for solving a hierarch variational inequality with constraints of variational inclusion and fixed point problems. J Inequal Appl. 2020;2020(1):1–9.
   Web of Science ®Google Scholar
• Muangchoo K, ur Rehman H, Kumam P. Two strongly convergent methods governed by pseudo-monotone bi-function in a real Hilbert space with applications. J Appl Math Comput. 2021.
   Web of Science ®Google Scholar
• Takahashi W, Wen C-F, Yao J-C. The shrinking projection method for a finite family of demimetric mappings with variational inequality problems in a Hilbert space. Fixed Point Theory. 2018;19(1):407–420.
   Web of Science ®Google Scholar
• ur Rehman H, Gibali A, Kumam P, et al. Two new extragradient methods for solving equilibrium problems. Rev R Acad Cienc Exactas Fıs Nat Ser A Mat. 2021;115(2):1–25.
   Web of Science ®Google Scholar
• ur Rehman H, Kumam P, Dong Q-L, et al. A modified self-adaptive extragradient method for pseudomonotone equilibrium problem in a real Hilbert space with applications. Math Methods Appl Sci. 2020;44(5):3527–3547.
   Web of Science ®Google Scholar
• ur Rehman H, Kumam P, Gibali A, et al. Convergence analysis of a general inertial projection-type method for solving pseudomonotone equilibrium problems with applications. J Inequal Appl. 2021;2021(1):1–27.
   Web of Science ®Google Scholar
• Zhao T-Y, Wang D-Q, Ceng L-C, et al. Quasi-inertial Tseng's extragradient algorithms for pseudomonotone variational inequalities and fixed point problems of quasi-nonexpansive operators. Numer Funct Anal Optim. 2021;42(1):69–90.
   Web of Science ®Google Scholar
• Antipin AS. On a method for convex programs using a symmetrical modification of the lagrange function. Ekonomika i Matematicheskie Metody. 1976;12(6):1164–1173.
   Google Scholar
• Polyak B. Some methods of speeding up the convergence of iteration methods. USSR Comput Math Math Phys. 1964;4(5):1–17.
   Google Scholar
• Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. Vol. 408. New York: Springer; 2011.
   Google Scholar
• Xu H-K. Another control condition in an iterative method for nonexpansive mappings. Bull Aust Math Soc. 2002;65(1):109–113.
   Web of Science ®Google Scholar
• Maingé P-E. Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization. Set-Valued Anal. 2008;16(7–8):899–912.
   Google Scholar
• Takahashi W. Nonlinear functional analysis. Yokohama; 2000.
   Google Scholar
• Liu H, Yang J. Weak convergence of iterative methods for solving quasimonotone variational inequalities. Comput Optim Appl. 2020;77(2):491–508.
   Web of Science ®Google Scholar
• Harker PT, Pang J-S. A damped Newton method for the linear complementarity problem. In: Computational solution of nonlinear systems of equations. Vol. 26. 1990. p. 265–284. New York: American Mathematical Society.
   Google Scholar
• Thong DV, Hieu DV, Rassias TM. Self adaptive inertial subgradient extragradient algorithms for solving pseudomonotone variational inequality problems. Optim Lett. 2019;14(1):115–144.
   Web of Science ®Google Scholar
• Anh PK, Thong DV, Vinh NT. Improved inertial extragradient methods for solving pseudo-monotone variational inequalities. Optimization. 2020;1–24. https://doi.org/10.1080/02331934.2020.1808644
   Web of Science ®Google Scholar
• Hu X, Wang J. Solving pseudomonotone variational inequalities and pseudoconvex optimization problems using the projection neural network. IEEE Trans Neur Netw. 2006;17(6):1487–1499.
   PubMed Web of Science ®Google Scholar
• Shehu Y, Dong Q-L, Jiang D. Single projection method for pseudo-monotone variational inequality in Hilbert spaces. Optimization. 2018;68(1):385–409.
   Web of Science ®Google Scholar