Viscosity method for hierarchical fixed point and variational inequalities with applications |
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| Authors: | Shi-sheng Zhang Xiong-rui Wang H. W. J. Lee Chi-kin Chan |
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| Affiliation: | 1. Department of Mathematics,Yibin University,Yibin 644007,Sichuan Province,P.R.China
2. Department of Applied Mathematics,The Hong Kong Polytechnic University,Hong Kong,P.R.China |
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| Abstract: | A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets. |
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| Keywords: | hierarchical fixed point non-expansive mapping fixed point viscosity approximation hierarchical minimization |
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