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应用数学学报  2014, Vol. 37 Issue (1): 160-169    DOI:
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解拟变分不等式的一种投影算法
叶明露1,2
1. 四川师范大学数学与软件科学学院, 成都 610068;
2. 西华师范大学数学与信息学院, 南充 637002
A Projection Method for Solving Quasi-variational Inequalities
YE Minglu1,2
1. Department of Mathematics, Sichuan Normal University, Chengdu 610068;
2. College of Mathematics, China West Normal University, Nanchong 637002
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摘要 本文通过构造能严格分离当前迭代点与拟变分不等式解集的超平面,并且利用当前迭代点向所构造的超平面与可行集的交做投影来产生新的迭代点,从而给出了求解拟变分不等式的一种新的投影算法. 在一定的假设条件下证明了该算法生成的无穷序列具有全局收敛性,数值试验表明该算法有较少的迭代步数.
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叶明露
关键词 拟变分不等式   广义Nash均衡   超平面   投影方法   收敛     
Abstract: We present a new projection method for solving quasi-variational inequalities. This new method consists of following two steps: First, we construct a hyperplane which can separate strictly current iterate from the solution set of the quasi-variational inequalities. Second, the next iterate is generated by projecting the current iterate onto the intersection of the feasible set C and this hyperplane. Our method is proven to be globally convergent under certain assumptions. Nnumerical experiments show that our method have the less total number of iterative steps.
Key wordsquasi-variational inequalities   generalized nash equilibrium   hyperplane   projection method   convergence   
收稿日期: 2006-01-09;
基金资助:国家自然科学基金(11271274)和西华师范大学科研启动基金(05B003)资助项目.
引用本文:   
叶明露. 解拟变分不等式的一种投影算法[J]. 应用数学学报, 2014, 37(1): 160-169.
YE Minglu. A Projection Method for Solving Quasi-variational Inequalities[J]. Acta Mathematicae Applicatae Sinica, 2014, 37(1): 160-169.
 
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