Convergence Rate of a Modified Extragradient Method for Pseudomonotone Variational Inequalities
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Anh, P.N., Muu, L.D., Nguyen, V.H., Strodiot, J.J.: Using the Banach contraction principle to implement the proximal point method for multivalued monotone variational inequalities. J. Optim. Theory Appl. 124, 285–306 (2005).
Gafni, E.M., Bertsekas, D.P.: Two-metric projection methods for constrained optimization. SIAM J. Control Optim. 22, 936–964 (1984).
Gafni, E.M., Bertsekas, D.P.: Two-metric projection problems and descent methods for asymmetric variational inequality problems. Math. Program. 53, 99–110 (1984).
Huy, N.Q., Yen, N.D.: Minimax variational inequalities. Acta Math. Vietnam. 36, 265–281 (2011).
Karamardian, S., Schaible, S.: Seven kinds of monotone maps. J. Optim. Theory Appl. 66, 37–46 (1990).
Khanh, P.D., Vuong, P.T.: Modified projection method for strongly pseudomonotone variational inequalities. J. Glob. Optim. 58, 341–350 (2014).
Khanh, P.D.: A modified extragradient method for infinite-dimensional variational inequalities. Acta Math. Vietnam. (2015). doi: 10.1007/s40306-015-0150-z .
Kim, D.S., Vuong, P.T., Khanh, P.D.: Qualitative properties of strongly pseudomonotone variational inequalities. Optim. Lett. (2015). doi: 10.1007/s11590-015-0960-x .
Kinderlehrer, D., Stampacchia, G.: An Introduction to Variational Inequalities and Their Applications. Academic Press, New York (1980).
Korpelevich, G.M.: An extragradient method for finding saddle points and for other problems. Ekon. Mat. Metod. 12, 747–756 (1976).
Muu, L.D., Quoc, T.D.: Regularization algorithms for solving monotone Ky Fan inequalities with application to a Nash-Cournot equilibrium model. J. Optim. Theory Appl. 142, 185–204 (2009).
Muu, L.D., Quy, N.V.: On existence and solution methods for strongly pseudomonotone equilibrium problems. Vietnam J. Math. 43, 229–238 (2015).
Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970).