Viscosity method for hierarchical fixed point and variational inequalities with applications |
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Authors: | ZHANG Shi-Sheng WANG Xiong-Rui HWJLEE CHEN Zhi-Jian |
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Institution: | 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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