| 关于变分与互补问题的线性逼近方法的收敛性分析 |
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| 引用本文： | 白中治 魏益民. 关于变分与互补问题的线性逼近方法的收敛性分析[J]. 复旦学报(自然科学版), 1997, 36(2): 206-218 |
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| 作者姓名： | 白中治 魏益民 |
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| 摘 要： | 建立了Ｐａｎｇ与Ｃｈａｎ提出了的求解变分不等问题的线性逼近方法的Ｋａｎｔｏｒｏｖｉｃｈ型收敛性理论，对于其特殊情形Ｎｅｗｔｏｎ法，刻划了其收敛速度及误差估计，给出了关一发不等问题的新型的解的的存在的唯一条件，且为迭代序列的初始选取提供了可靠的依据。
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| 关 键 词： | 变分不等式 互补问题 线性逼近 收敛性 |
On the convergence of the linear approximation methods for variational and complementarity problems |
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| Bai Zhongzhi, Wei Yimin. On the convergence of the linear approximation methods for variational and complementarity problems[J]. Journal of Fudan University(Natural Science), 1997, 36(2): 206-218 |
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| Authors: | Bai Zhongzhi Wei Yimin |
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| Affiliation: | Institute of Mathematics |
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| Abstract: | This paper thoroughly establishes the Kantorovich-type convergence theories for the linear approximation methods (LAMs) set up by Pang and Chan in 1982 for solving the variational inequality problems. For the important special case Newton method, the convergence rate and error estimate are particularly described in precision and detail. This work, besides giving new existence and uniqueness conditions for the solution of the variational inequality problem, also affords reliable principles for the choices of the starting vectors of the iterations. |
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| Keywords: | variational inequality nonlinear complementarity problem linear approximation method Kantorovich-type convergence analysis |
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