An operator splitting method for variational inequalities with partially unknown mappings |
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| Authors: | Deren Han Wei Xu Hai Yang |
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| Affiliation: | (1) School of Mathematics and Computer Sciences, Nanjing Normal University, 210097 Nanjing, People’s Republic of China;(2) School of Management and Engineering, Nanjing University, 210093 Nanjing, People’s Republic of China;(3) Department of Civil Engineering, The Hong Kong University of Science and Technology, Hong Kong, People’s Republic of China |
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| Abstract: | In this paper, we propose a new operator splitting method for solving a class of variational inequality problems in which part of the underlying mappings are unknown. This class of problems arises frequently from engineering, economics and transportation equilibrium problems. At each iteration, by using the information observed from the system, the method solves a system of nonlinear equations, which is well-defined. Under mild assumptions, the global convergence of the method is proved, and its efficiency is demonstrated with numerical examples. The research of D. Han is supported by NSFC grant 10501024 and NSF of Jiangsu Province at Grant No. BK2006214. |
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| Keywords: | KeywordHeading" >Mathematics Subject Classification (2000) 90C33 65K05 |
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