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求解强单调变分不等式组的一种自适应投影算法 被引量：1

A Self-adaption Projection Algorithm for System of Strongly Monotone Variational Inequalities
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摘要 自适应投影算法是求解强单调变分不等式的一种重要方法,在自然科学中的诸多领域有着广泛的应用.利用自适应投影算法来求解强单调变分不等式组.从理论上证明了这种算法的收敛性,结果推广了He,Yang,Meng和Han的结论. Self - adaption projection algorithm is an attractive method for solving strongly monotone variational inequalities, it can be applied to a large number of fields of natural science. In this paper, the system of strongly monotone variational inequalities by using a selfadaptive projection method is studied. Theoretically, the convergence of this algorithm is proved. The results presented in this paper extend corresponding results of He, Yang, Meng and Han.
作者 郑海燕 赵世莲
机构地区 西华师范大学数学与信息学院
出处 《绵阳师范学院学报》 2013年第2期17-21,共5页 Journal of Mianyang Teachers＇ College
基金 教育部科学技术重点项目(211163) 四川省青年科技基金(2012JQ0032)
关键词 变分不等式组 投影算法 全局收敛性 System of variational inequality projection Algorithm global convergence
分类号 O221 [理学—运筹学与控制论]
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参考文献9

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同被引文献9

  • 1ARMIJO L. Minimization of Funtions Having Continuous Partial Derivatives[ J]. Pacific Journal of Mathematics, 1966,16 : 1 - 3.
  • 2BERTSEKAS D P. On the Goldstein-Levitin-Polyak Gradient Projection Method[ J]. IEEE Transactions on Automatic Control, 1976,21 : 174 - 184.
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  • 4GOLDSTEIN A A. Convex Programming in Hilbert Space [ J ]. Bulletin of the American Mathematical Society, 1964,70:709 -710.
  • 5HE B S, YANG H, MENG Q,et al. Modified Goldstein-Levitin-Polyak Projection Method for Asymmetric Strongly Monotone Vari- ational Inequalities[ J]. Journal of Optimization Theory and Applications,January 2002,112 ( 1 ) :29 -143.
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  • 7KORPELEVICH G M. The Extragradient Method for Finding Saddle Points and Other Problems[ J]. Mateeon ,1976 ,12 :747 -756.
  • 8KHOBOTOV E N. Modification of the Extragradient Method for Solving Variational Inequalities and Certain Optimization Prob- lems[ J]. USSR Computational Mathematics and Mathematical Physics, 1987,27 : 120 - 127.
  • 9LEVITIN E S,POLYAK B T. Constrained Minimization Problems[ J]. USSR Computational Mathematics and Mathematical Phys- ics. 1996.6 : 1 - 50.

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绵阳师范学院学报
2013年 第2期

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