Self-adaptive projection method for co-coercive variational inequalities |
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Authors: | Bingsheng He Xiao-Zheng He Henry X. Liu Ting Wu |
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Affiliation: | 1. Department of Mathematics, Nanjing University, Nanjing 210093, China;2. Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55455, USA |
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Abstract: | In some real-world problems, the mapping of the variational inequalities does not have any explicit forms and only the function value can be evaluated or observed for given variables. In this case, if the mapping is co-coercive, the basic projection method is applicable. However, in order to determine the step size, the existing basic projection method needs to know the co-coercive modulus in advance. In practice, usually even if the mapping can be characterized co-coercive, it is difficult to evaluate the modulus, and a conservative estimation will lead an extremely slow convergence. In view of this point, this paper presents a self-adaptive projection method without knowing the co-coercive modulus. We also give a real-life example to demonstrate the practicability of the proposed method. |
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Keywords: | 65K10 90C25 90C30 |
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