Implicit and explicit iterative algorithms for hierarchical variational inequality in uniformly smooth Banach spaces.
作者： Lu-Chuan Ceng , Yung-Yih Lur , Ching-Feng Wen
DOI: 10.1186/S13660-017-1523-8
关键词:
摘要: The purpose of this paper is to solve the hierarchical variational inequality with constraint a general system inequalities in uniformly convex and 2-uniformly smooth Banach space. We introduce implicit explicit iterative algorithms which converge strongly unique solution problem. Our results improve extend corresponding announced by some authors.
springeropen.com
springer.com
core.ac.uk 
sci-hub.se 参考文章(31)
Ioana Ciorănescu, Geometry of banach spaces, duality mappings, and nonlinear problems ,(1990)
G. M. Korpelevich, The extragradient method for finding saddle points and other problems Matecon. ,vol. 12, pp. 747- 756 ,(1976)
Francisco Facchinei, Jong-Shi Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems ,(2003)
Isao Yamada, The Hybrid Steepest Descent Method for the Variational Inequality Problem Over the Intersection of Fixed Point Sets of Nonexpansive Mappings Studies in Computational Mathematics. ,vol. 8, pp. 473- 504 ,(2001) , 10.1016/S1570-579X(01)80028-8
Yonghong Yao, Mihai Postolache, Yeong-Cheng Liou, Zhangsong Yao, Construction algorithms for a class of monotone variational inequalities Optimization Letters. ,vol. 10, pp. 1519- 1528 ,(2016) , 10.1007/S11590-015-0954-8
Wataru Takahashi, Misako Kikkawa, STRONG CONVERGENCE THEOREMS BY THE VISCOSITY APPROXIMATION METHOD FOR A COUNTABLE FAMILY OF NONEXPANSIVE MAPPINGS Taiwanese Journal of Mathematics. ,vol. 12, pp. 583- 598 ,(2008) , 10.11650/TJM.12.2008.599
Nguyen Buong, Nguyen Thi Quynh Anh, An Implicit Iteration Method for Variational Inequalities over the Set of Common Fixed Points for a Finite Family of Nonexpansive Mappings in Hilbert Spaces Fixed Point Theory and Applications. ,vol. 2011, pp. 276859- ,(2011) , 10.1155/2011/276859
Yonghong Yao, Yeong-Cheng Liou, Shin Min Kang, Youli Yu, Algorithms with strong convergence for a system of nonlinear variational inequalities in Banach spaces Nonlinear Analysis: Theory, Methods & Applications. ,vol. 74, pp. 6024- 6034 ,(2011) , 10.1016/J.NA.2011.05.079
Lu-Chuan Zeng, Jen-Chih Yao, Implicit iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings Nonlinear Analysis-theory Methods & Applications. ,vol. 64, pp. 2507- 2515 ,(2006) , 10.1016/J.NA.2005.08.028
Yonghong Yao, Muhammad Aslam Noor, Yeong-Cheng Liou, Strong Convergence of a Modified Extragradient Method to the Minimum-Norm Solution of Variational Inequalities Abstract and Applied Analysis. ,vol. 2012, pp. 1- 9 ,(2012) , 10.1155/2012/817436