JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (2): 38-45.doi: 10.6040/j.issn.1671-9352.0.2017.310
Previous Articles Next Articles
YANG Yan-tao
CLC Number:
| [1] KORPELEVICH G M.An extragradient method for finding saddle points and other problems[J]. Ekonomikai Matematicheskie Metody, 1976, 12(4):747-756. [2] NADEZHKINA N, TAKAHASHI W. Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings[J]. Journal of Optimization Theory and Applications, 2006, 128(1):191-201. [3] TAKAHASHI W, TOYODA M. Weak convergence theorems for nonexpansive mappings and monotone mappings[J]. Journal of Optimization Theory and Applications, 2003, 118(2):417-428. [4] CENSOR Y, GIBALI A, REICH S. Extensions of Korpelevichs extragradient method for the variational inequality problem in Euclidean space[J]. Optimization, 2010, 61(9):1119-1132. [5] HE Songnian, YANG Caiping. Solving the variational inequality problem defined on intersection of finite level sets[J]. Abstract and Applied Analysis, 2013, 12(2):94-121. [6] HE Songnian, XU Hongkun. The supporting hyperplane and an alterntive to solutions of variational inequalities[J]. Journal of Nonlinear and Convex Analysis, 2015, 16(11):2323-2331. [7] CAI Gang, YEKINI Shehe, IYIOLA Olaniyi Samuel. Iterative algorithms for solving variational inequalities and fixed point problems for asymptotically nonexpansive mappings in Banach spaces[J]. Numerical Algorithms, 2016, 73(3):869-906. [8] CEGIELSKI A, ZALAS R. Methods for variational inequality problem over the intersection of fixed point sets of quasi-nonexpansive operators[J]. Numerical Functional Analysis and Optimization, 2013, 34(3):255-283. [9] CRUZ J Y B, IUSEM A N. A strong convergent direct method for monotone variational inequalities in Hilbert spaces[J]. Numerical Functional Analysis and Optimization, 2009, 30(1):23-36. [10] IUSEM A N, NASRI M. Kropelevichs method for variational inequality problems in Banach spaces[J]. Journal of Global Optimization, 2011, 50(1):59-76. [11] TANG Guoji, HUANG Nanjing. Kropelevichs method for variational inequality problems on Hadamard manifolds[J]. Journal of Global Optimization, 2012, 54(3):493-509. [12] TANG Guoji, WANG Xing, LIU Huanwen. A projection-type method for variational inequalities on Hadamard manifolds and verification of solution existence[J]. Optimization, 2013, 64(5):1081-1096. [13] IUSEM A N, SVAITER B F. A variant of Korpelevichs method for variational inequalities with a new search strategy[J]. Optimization, 1997, 42(2):309-321. [14] SOLODOV M V, SVAITER B F. A new projection method for variational inequality problems[J]. Siam Journal on Control and Optimization, 1999, 37(3):765-776. [15] HE Yiran. A new double projection algorithm for variational inequality[J]. Journal of Computational and Applied Mathematics, 2006, 185(1):166-173. [16] CENSOR Y, GIBALI A, REICH S. The subgradient extragradient method for solving variational inequalities in Hilbert space[J]. Journal of Optimization Theory and Applications, 2011, 148(2):318-335. [17] 周海云.不动点与零点的迭代方法及其应用[M].北京:国防工业出版社,2016. ZHOU Haiyun. Iterative methods of fixed points and zeros with applications[M]. Beijing: National Defend Industry Press, 2016. [18] ZHOU Haiyun, ZHOU Yu, FENG Guanghui. Iterative methods for solving a class of monotone variational inequality problems with applications[J]. Journal of Inequalities and Applications, 2015, 2015(68):1-17. [19] HE Songnian, WU Tao. A modified subgradient extragradient method for solving monotone variational inequalities[J]. Journal of Inequalities and Applications, 2017, 2017(89):1-14. [20] TAKAHASHI S, TAKAHASHI W. Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces[J]. Journal of Mathematical Analysis and Applications, 2007, 331(1):506-515. [21] YAO Yonghong, LIOU Yeong Cheng, KANG Shin Min. Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method[J]. Computers and Mathematics with Applications, 2010, 59(11):3472-3480. [22] MOUDAFI A. Split Monotone Variational inclusions[J]. Journal of Optimization Theory and Applications, 2011, 150(2):275-283. [23] ANSARI Q H, REHAN A. An iterative method for split hierarchical monotone variational inclusions[J]. Fixed Point Theory and Applications, 2015, 2015(121):1-10. [24] OPIAL Z. Weak convergence of the sequence of successive approximations for nonexpansive mappings[J]. Bulletin of the American Mathematical Society, 1967, 73(4):591-597. [25] BROWDER F E. Nonexpansive nonlinear operators in a Banach space[J]. Proceedings of the National Academy of Sciences of the United States of America, 1965, 54(4):1041-1044. [26] HE Songnian, XU Hongkun. Uniqueness of supporting hyperplanes and an alternative to solutions of variational inequalities[J]. Journal of Global Optimization, 2013, 57(4):1375-1384. |
| [1] | LI Ai-qin,FAN Li-ya . Relations of generalized invariant monotonicity and invexity [J]. J4, 2008, 43(5): 71-74 . |
| [2] | . Modified threestep iterative method for solving variational inequalities [J]. J4, 2009, 44(6): 69-74. |
|
||
