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解变分不等式的三步松弛混合最速下降法

丁协平 林炎诚 姚任之

丁协平, 林炎诚, 姚任之. 解变分不等式的三步松弛混合最速下降法[J]. 应用数学和力学, 2007, 28(8): 921-928.
引用本文: 丁协平, 林炎诚, 姚任之. 解变分不等式的三步松弛混合最速下降法[J]. 应用数学和力学, 2007, 28(8): 921-928.
DING Xie-ping, LIN Yen-cherng, YAO Jen-chih. Three-Step Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities[J]. Applied Mathematics and Mechanics, 2007, 28(8): 921-928.
Citation: DING Xie-ping, LIN Yen-cherng, YAO Jen-chih. Three-Step Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities[J]. Applied Mathematics and Mechanics, 2007, 28(8): 921-928.

解变分不等式的三步松弛混合最速下降法

基金项目: 四川省教育厅重点科研基金资助项目(2003A081);四川重点学科基金资助项目(0406)
详细信息
    作者简介:

    丁协平(1938- ),男,自贡人,教授(联系人.Tel:+86-28-84780952;E-mail:xieping.ding@hotmail.com);林炎诚(1963- ),男,副教授;姚任之(1959- ),男,高雄人,教授,博士生导师.

  • 中图分类号: O177.92

Three-Step Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities

  • 摘要: 在Hilbert空间的非空闭凸子集上研究了具有Lipschitz和强单调算子的经典变分不等式.为求解此变分不等式引入了一类新的三步松弛混合最速下降法.在算法参数的适当假设下,证明了此算法的强收敛性.
  • [1] Kinderlehrer D, Stampacchia G.An Introduction to Variational Inequalities and Their Applications[M].New York: Academic Press, 1980.
    [2] 张石生.变分不等式和相补问题理论及应用[M].上海:上海科技文献出版社,1991.
    [3] Glowinski R.Numerical Methods for Nonlinear Variational Problems[M].New York: Springer, 1984.
    [4] Jaillet P, Lamberton D,Lapeyre B.Variational inequalities and the pricing of American options[J].Acta Applicandae Mathematicae,1990,21(2):263-289. doi: 10.1007/BF00047211
    [5] Konnov I.Combined Relaxation Methods for Variational Inequalities[M].Berlin: Springer, 2001.
    [6] Oden J T.Qualitative Methods on Nonlinear Mechanics[M]. New Jersey: Prentice-Hall, Englewood Cliffs, 1986.
    [7] Zeng L C. Iterative algorithm for finding approximate solutions to completely generalized strongly nonlinear quasivariational inequalities[J].Journal of Mathematical Analysis and Applications,1996,201(1):180-194. doi: 10.1006/jmaa.1996.0249
    [8] Zeng L C. Completely generalized strongly nonlinear quasi-complementarity problems in Hilbert spaces[J].Journal of Mathematical Analysis and Applications,1995,193(3):706-714. doi: 10.1006/jmaa.1995.1262
    [9] Zeng L C. On a general projection algorithm for variational inequalities[J].Journal of Optimization Theory and Applications,1998,97(2):229-235. doi: 10.1023/A:1022687403403
    [10] Xu H K, Kim T H.Convergence of hybrid steepest-descent methods for variational inequalities[J].Journal of Optimization Theory and Applications,2003,119(1):185-201. doi: 10.1023/B:JOTA.0000005048.79379.b6
    [11] Yamada I. The hybrid steepest-descent method for variational inequality problems over the intersection of the fixed-point sets of nonexpansive mappings[A].In:Butnariu D,Censor Y,Reich S,Eds.Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications[C]. Amsterdam: North-Holland, 2001, 473-504.
    [12] Zeng L C, Wong N C,Yao J C. Convergence analysis of modified hybrid steepest-descent methods with variable parameters for variational inequalities[J].Journal of Optimization Theory and Applications,2007,132(1):51-69. doi: 10.1007/s10957-006-9068-x
    [13] Xu H K. Iterative algorithms for nonlinear operators[J].Journal of London Mathematical Society,2002,66(2):240-256. doi: 10.1112/S0024610702003332
    [14] Geobel K, Kirk W A.Topics on Metric Fixed-Point Theory[M].Cambridge: Cambridge University Press, 1990.
    [15] Yao J C. Variational inequalities with generalized monotone operators[J].Mathematics of Operations Research,1994,19:691-705. doi: 10.1287/moor.19.3.691
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出版历程
  • 收稿日期:  2006-11-19
  • 修回日期:  2007-06-25
  • 刊出日期:  2007-08-15

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