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求解单调变分不等式的近似邻近点算法的收敛性分析 被引量：2

The convergence analysis of an approximate proximal point algorithm for monotone variational inequalities
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摘要 为了求解单调变分不等式,建立了一个新的误差准则,并且在不需要增加诸如投影,外梯度等步骤的情况下证明了邻近点算法的收敛性. In this paper, a new error criterion of approximate proximal point algorithm for solving monotone variational inequalities is constructed, and the convergence of the algorithm is proved, where indirect step, such as projection step, extragradient step, is not required.
作者 唐国吉
机构地区 广西民族大学数学与计算机科学学院
出处 《纯粹数学与应用数学》 CSCD 2009年第1期183-189,共7页 Pure and Applied Mathematics
基金 广西民族大学青年科学基金(2007QN25).
关键词 变分不等式 邻近点算法 收敛性 variational inequalities, proximal point algorithm, convergence
分类号 O224 [理学—运筹学与控制论]
  • 相关文献

参考文献11

  • 1齐成辉,石超峰.广义集值变分不等式的一类新的外梯度算法[J].纯粹数学与应用数学,2006,22(2):194-197. 被引量：2
  • 2黄龙光.半准内凸函数及其广义变分不等式[J].纯粹数学与应用数学,2001,17(4):314-317. 被引量：1
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  • 4He Bingsheng, Qian Maijian, Wang Yumei. Study on approximate proximal point algorithms for monotone variational inequalities[M]//Yuan Yaxiang. Numerical Linear Algebra and Optimization. Beijing: Science Press,2004.
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  • 6何炳生,杨振华,廖立志.极大单调算子的一个新的近似邻近点算法[J].中国科学（A辑）,2002,32(11):1026-1032. 被引量：13
  • 7王治华.关于单调变分不等式的不精确邻近点算法的收敛性分析[J].高等学校计算数学学报,2003,25(4):336-343. 被引量：8
  • 8Han Deren, He Bingsheng. A new accuracy criterion for approximate proximal point algorithms[J]. Journal of Mathematical Analysis and Applications,2001,263:343-354.
  • 9Solodov M V. Switer B F. A hybrid projection-proximal point algorithm[J]. Journal of Convex Analysis,1999, 6(1):59-70.
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二级参考文献30

  • 1[1]Brezis H. Operateurs Maximaux Monotone et Semi-Groups de Contractions dans les Espaces de Hilbert.Amsterdam: North-Holland, 1973
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共引文献15

同被引文献21

  • 1高雷阜,王金希,吴洪涛.Banach空间中一类变分包含解的存在性和唯一性[J].辽宁工程技术大学学报（自然科学版）,2012,31(2):252-255. 被引量：8
  • 2Noor M A.General variational inequalities[J].Applied Mathematics Letters,1988(1): 119-121.
  • 3Martinet B.Regularization d'inequafions variationelles par approximations sucessives[J].Revue Francaise d'Informatique et de Recherche Operationelle, 1970,4:154-159.
  • 4Solodov M V, Svaiter B F.Error bounds for proximal point subproblems and associated inexact proximal point algorithms[J].Mathematical Programming,2000,88(8):371-389.
  • 5Solodov M V, Svaiter B F.A unified framework for some inexact proximal point algorithms[J].Numerical Functional Analysis and Optimization,2001,22:1013 - 1035.
  • 6Rockefeller R T.Monotone operators and the proximal point algorithm [J].Journal on Control and Optimization, 1976,14(5):877-898.
  • 7Eckstein J.Approximate iterations in Bergman-funefion-based proximal algorithms [J] .Mathematical Programming, 1998,83:113 - 123.
  • 8Han D R,He B S.A new accuracy criterion for approximate proximal point algorithms[J].Journal of Mathematical Analysis and Applications,2001,263: 343-354.
  • 9He B S,Qian M J,Wang Y M.Numerical Linear Algebra and Optimization:Study on Approximate Proximal Point Algorithms for Monotone Variational Inequalities[M].Beijing:Science Press,2004.
  • 10刘鲭洁,陈桂明,杨旗.基于Matlab工具的遗传算法求解有约束最优化问题[J].兵工自动化,2008,27(11):43-44. 被引量：10

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纯粹数学与应用数学
2009年 第1期

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