| 变分不等式的一类二次投影算法 |
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| 引用本文： | 叶明露.变分不等式的一类二次投影算法[J].应用数学学报,2012,35(3):529-535. |
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| 作者姓名： | 叶明露 |
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| 作者单位： | 四川师范大学数学与软件科学学院,成都610068;西华师范大学数学与信息学院,南充637002 |
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| 摘 要： | 通过构造的一类严格分离当前点与解集的超平面得到了一类解伪单调变分不等式的修正二次投影算法,该算法对He Yiran的算法进行了修正.从而建立了解伪单调变分不等式二次投影算法的一种框架结构.证明了该算法生成的无穷序列具有的全局收敛性,在具备某种局部误差界和Lipchitz连续条件下给出了收敛率分析.并给出了该算法的数值演算结果.
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| 关 键 词： | 变分不等式 二次投影算法 伪单调 |
The Framework of Double Projection Algorithm for Variational Inequalities |
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| YE MINGLU.The Framework of Double Projection Algorithm for Variational Inequalities[J].Acta Mathematicae Applicatae Sinica,2012,35(3):529-535. |
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| Authors: | YE MINGLU |
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| Institution: | YE MINGLU (Department of Mathematics,Sichuan Normal University,Chengdu 610068) (College of Mathematics,China WestNormal University,Nanchong 637002) |
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| Abstract: | We present a modification of a double projection algorithm proposed by Yiran He for solving pseudomonotone variational inequalities.The main modification is obtained a class of hyperplane,which can separate the current iterate from the solution of the variational inequalities.To use these hyperplanes,we construct the framework of double projection algorithm for solving variational inequalities.Our method is proven to be globally convergent under very mild assumptions.If in addition a certain error bound holds,we analyze the convergence rate of the iterative sequence.Numerical experiments are proposed too. |
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| Keywords: | variational inequalities double projection algorithm pseudo-monotone |
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