References
- Takahashi W, Toyoda M. Weak convergence theorems for nonexpansive mappings and monotone mappings. J. Optim. Theor. Appl. 2003;118:417–428.
- Iiduka H, Takahashi W. Strong convergence theorems for nonexpansive nonself-mappings and inverse-strongly-monotone mappings. J. Convex Anal. 2004;11:69–79.
- Iiduka H, Takahashi W. Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings. Nonlinear Anal. Theor. Meth. Appl. 2005;61:341–350.
- 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.
- Nadezhkina N, Takahashi W. Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings. J. Optim. Theor. Appl. 2006;128:191–201.
- Ceng LC, Yao JC. Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems. Taiwanese J. Math. 2006;10:1293–1303.
- Yao YH, Yao JC. On modified iterative method for nonexpansive mappings and monotone mappings. Appl. Math. Comput. 2007;186:1551–1558.
- Ceng LC, Hadjisavvas N, Wong NC. Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems. J. Global Optim. 2010;46:635–646.
- Censor Y, Gibali A, Reich S. The subgradient extragradient method for solving variational inequalities in Hilbert space. J. Optim. Theor. Appl. 2011;148:318–335.
- Korpelevich GM. The extragradient method for finding saddle points and others problems. Matecon. 1976;17:747–756.
- Liu LW, Li YQ. On generalized set-valued variational inclusions. J. Math. Anal. Appl. 2001;261:231–240.
- Solodov MV, Svaiter BF. A new projection method for variational inequality problems. SIAM J. Contr. Optim. 1999;37:765–776.
- He BS. A class of projection and contraction methods for monotone variational inequalities. Appl. Math. Optim. 1997;35:69–76.
- He YR. A new double projection algorithm for variational inequality. J. Comput. Appl. Math. 2006;185:166–173.
- 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.
- Facchinei F, Pang JS. Finite-dimensional variational inequalities and complementarity problems. New York (NY): Springer-Verlag; 2003.
- Brower FE. Multi-valued monotone nonlinear mapping and duality mappings in Banach space. Trans. Am. Math. Soc. 1965;118:338–351.
- Konnov IV. On the rate of convergence of combined relaxation methods. Izvestiya Vysshikh Uchebnykh Zavedeii. Matematika. 1993;37:89–92.
- Konnov IV. Combined relaxation methods for variational inequalities. Berlin: Springer-Verlag; 2001.
- Allevi E, Gnudi A, Konnov IV. The proximal point method for nonmonotone variational inequalities. Math. Meth. Oper. Res. 2006;63:553–565.
- Konnov IV. Combined relaxation methods for generalized monotone variational inequalities. In: Generalized convexity and related topics. Vol. 583, Lecture notes in economics and mathematics systems. Berlin: Springer; 2007. p. 3–31.
- Ceng LC, Yao JC. Approximate proximal algorithms for generalized variational inequalities with pseudomonotone multifunctions. J. Comput. Appl. Math. 2008;213:423–438.
- Ceng LC, Lai TC, Yao JC. Approximate proximal algorithms for generalized variational inequalities with paramonotonicity and pseudomonotonicity. Comput. Math. Appl. 2008;55:1262–1269.
- Xia FQ, Huang NJ. A projection-proximal point algorithm for solving generalized variational inequalities. J. Optim. Theor. Appl. 2011;150:98–117.
- Rockfellar RT. Monotone operators and the proximal point algorithm. SIAM J. Contr. Optim. 1976;14:877–898.
- Li FL, He YR. An algorithm for generalized variational inequality with pseudomonotone mapping. J. Comput. Appl. Math. 2009;228:212–218.
- Fang CJ, He YR. A double projection algorithm for multi-valued variational inequalities and a unified framework of the method. Appl. Math. Comput. 2011;217:9543–9551.
- Takahashi W. Nonlinear functional analysis. Yokohama: Yokohama Publishers; 2000.
- Brower FE. Fixed point theorems for noncompact mappings in Hilbert space. Proc. Natl. Acad. Sci. USA. 1965;53:1272–1276.
- Polyak BT. Introduction to optimization. New York (NY): Optimization Software, Publications Division; 1987.
- Aubin JP, Ekeland I. Applied nonlinear analysis. Pure and applied mathematics. New York (NY): Wiley; 1984.