[1] Iiduka H.Acceleration method for convex optimization over the fixed point set of a nonexpansive mapping. Mathematical Programming, 2015, 149(1): 131-165
[2] Maingé P E.A hybrid extragradient-viscosity method for monotone operators and fixed point problems. SIAM Journal on Control and Optimization, 2008, 47(3): 1499-1515
[3] Thong D V, Hieu D V.Modified subgradient extragradient algorithms for variational inequality problems and fixed point problems. Optimization, 2018, 67(1): 83-102
[4] Nadezhkina N, Takahashi W.Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings. Journal of Optimization Theory and Applications, 2006, 128: 191-201
[5] Takahashi W, Toyoda M.Weak convergence theorems for nonexpansive mappings and monotone mappings. Journal of Optimization Theory and Applications, 2003, 118: 417-428
[6] Thong D V, Hieu D V. New extragradient methods for solving variational inequality problems and fixed point problems. Journal of Fixed Point Theory and Applications, 2018, 20(3): Article 129
[7] Thong D V, Hieu D V.Some extragradient-viscosity algorithms for solving variational inequality problems and fixed point problems. Numerical Algorithms, 2019, 82(3): 761-789
[8] Thong D V, Liu L L, Dong Q L, et al.Fast relaxed inertial Tseng's method-based algorithm for solving variational inequality and fixed point problems in Hilbert spaces. Journal of Computational and Applied Mathematics, 2023, 418: 114739
[9] 段洁, 夏福全. 求解变分不等式与不动点问题公共解的新 Tseng 型外梯度算法. 数学物理学报, 2023, 43A(1): 274-290
Duan J, Xia F Q.A new Tseng-like extragradient algorithm for common solutions of variational inequalities and fixed point problems. Acta Math Sci, 2023, 43A(1): 274-290
[10] Goldstein A A.Convex programming in Hilbert space. Bulletin of the American Mathematical Society, 1964, 70(5): 109-112
[11] Mann W R.Mean value methods in iteration. Proceedings of the American Mathematical Society, 1953, 4(3): 506-510
[12] Korpelevich G M.The extragradient method for finding saddle points and other problems. Matecon, 1976, 12: 747-756
[13] Censor Y, Gibali A, Reich S.The subgradient extragradient method for solving variational inequalities in Hilbert space. Journal of Optimization Theory and Applications, 2011, 148(2): 318-335
[14] Tseng P.A modified forward-backward splitting method for maximal monotone mappings. SIAM Journal on Control and Optimization, 2000, 38(2): 431-446
[15] Halpern B.Fixed points of nonexansive maps. Bulletin of the American Mathematical Society, 1967, 73: 957-961
[16] Wang Z B, Chen X, Yi J, Chen Z Y.Inertial projection and contraction algorithms with larger step sizes for solving quasimonotone variational inequalities. Journal of Global Optimization, 2022, 82(3): 499-522
[17] Yin T C, Wu Y K, Wen C F.An iterative algorithm for solving fixed point problems and quasimonotone variational inequalities. Journal of Mathematics, 2022, 2022(1): 8644675
[18] Chidume C E, Măuşter Ş.Iterative methods for the computation of fixed points of demicontractive mappings. Journal of Computational and Applied Mathematics, 2010, 234(3): 861-882
[19] Mongkolkeha C, Cho Y J, Kumam P.Convergence theorems for k-dimeicontactive mappings in Hilbert spaces. Mathematical Inequalities & Applications, 2013, 16(4): 1065-1082
[20] Kraikaew R, Saejung S.Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Hilbert spaces. Journal of Optimization Theory and Applications, 2014, 163: 399-412
[21] Tian M, Xu G. Inertial modified Tseng's extragradient algorithms for solving monotone variational inequalities and fixed point problems. J Nonlinear Funct Anal, 2020, 2020: Article 35
[22] Bauschke H H, Combettes P L.Convex Analysis and Monotone Operator Theory in Hilbert Spaces. New York: Springer, 2011
[23] Denisov S V, Semenov V V, Chabak L M.Convergence of the modified extragradient method for variational inequalities with non-Lipschitz operators. Cybernetics and Systems Analysis, 2015, 51: 757-765
[24] Saejung S, Yotkaew P.Approximation of zeros of inverse strongly monotone operators in Banach spaces. Nonlinear Analysis: Theory, Methods & Applications, 2012, 75(2): 742-750
[25] Ye M L.An infeasible projection type algorithm for nonmonotone variational inequalities. Numerical Algorithms, 2022, 89(4): 1723-1742
[26] Ye M L, He Y R.A double projection method for solving variational inequalities without monotonicity. Computational Optimization and Applications, 2015, 60(1): 141-150
[27] Iusem A, Otero R G.Inexact versions of proximal point and augmented Lagrangian algorithms in Banach spaces. Numerical Functional Analysis and Optimization, 2001, 22(5/6): 609-640
[28] Cai G, Dong Q L, Peng Y.Strong convergence theorems for solving variational inequality problems with pseudo-monotone and non-Lipschitz operators. Journal of Optimization Theory and Applications, 2021, 188: 447-472
[29] Shehu Y, Dong Q L, Jiang D.Single projection method for pseudo-monotone variational inequality in Hilbert spaces. Optimization, 2019, 68(1): 385-409
[30] Rehman H U, Kumam P, Kumam W, Sombut K.A new class of inertial algorithms with monotonic step sizes for solving fixed point and variational inequalities. Mathematical Methods in the Applied Sciences, 2022, 45(16): 9061-9088
[31] 杨静, 龙宪军. 关于伪单调变分不等式与不动点问题的新投影算法. 数学物理学报, 2022, 42A(3): 904-919
Yang J, Long X J.A new projection algorithm for solving pseudo-monotone variational inequality and fixed point problems. Acta Math Sci, 2022, 42A(3): 904-919 |