期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

随机规划逼近问题最优解集的稳定性 被引量：2

Stability of the Optimal Solution Sets of Approximation Problems for Stochastic Programming
原文传递
导出
摘要 讨论了参数规划问题最优解集的连续性,并利用集值分析理论证明了随机规划最优解集对所含随机变量参数的分布收敛、概率收敛、几乎处处收敛的稳定性。 The continuity properties of optimal solution sets in parametric programming problems are discussed. Relying on the theory of set-valued analysis, we have obtained corresponding stability results of the optimal solution sets of stochastic programming when the random variable parameter is convergence in distribution, convergence in probability and almost everywhere convergence, respectively.
作者 霍永亮 刘三阳
机构地区 重庆文理学院数学与统计学院 西安电子科技大学应用数学系
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2009年第5期911-918,共8页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金(60574075) 重庆市教委基金(09KJ091211) 重庆文理学院引进人才资助项目
关键词 随机规划 稳定性 分布收敛 stochastic programming stability convergence in distribution
分类号 O221.5 [理学—运筹学与控制论]
  • 相关文献

参考文献14

  • 1Rachev S. T., Romisch,W., Quantitative stability in stochastic programming: the method of probability metrics, Mathematics of Operations Research, 2002, 27(4): 792-818.
  • 2Henrion R., Romisch W., HSlder and Lipschitz stability of solution sets in programs with probabilistic constraints, Mathematical Programming, 2004, 100(3): 589-611.
  • 3Romisch W., Wets R. J. B., Stability of e-approximate solutions to convex stochastic programs, SIAM Journal on Optimization, 2007, 18: 961-979.
  • 4Heitsch H., Romisch W., Strugarek C., Stability of multistage stochastic programs, SIAM Journal on Optimization, 2006, 17: 511-525.
  • 5Eichhorn A., RSmisch W., Stochastic integer programming: limit theorems and confidence intervals, Mathematics of Operations Research, 2007, 32: 118-135.
  • 6Heitsch H., Romisch W., A note on scenario reduction for two-stage stochastic programs, Operations Research Letters, 2007, 18: 961-979.
  • 7Salinetti G., Wets R. J. B., On the convergence in distribution of measurable multifunctions, normal integrands, stochastic processes and stochastic infima, Mathematics of Operations Research, 1986, 11(3): 385- 419.
  • 8Vogel S., A Stochastic approach to stability in stochastic programmin g, Journal of Computational Applied Mathematics, 1994, 56(1): 65-96.
  • 9Li L., Wu C. X., Set-valued Analysis, Beijing: Science Press, 2003.
  • 10Bank B., Cuddat J., Klatte D., Non-Linear Parametric Optimization, Berlin: Akademie-Verlag, 1983.

同被引文献11

  • 1霍永亮,刘三阳.随机规划逼近最优解集的上半收敛性[J].西安电子科技大学学报,2005,32(6):953-957. 被引量：17
  • 2霍永亮,刘三阳.概率约束规划逼近最优解集的上半收敛性[J].应用数学,2006,19(2):263-269. 被引量：1
  • 3霍永亮,刘三阳.随机规划经验逼近最优解集序列的几乎处处上半收敛性[J].工程数学学报,2007,24(4):701-706. 被引量：4
  • 4Romisch W.H61der and Lipschitz Stability of Solution Sets in Programs with Probabilistie Constraints[J].Mathematical Programming,2004,100(3):589-611.
  • 5Pennanen T,Koivu M.Epi-convergent Discretizations of Stochastic Programs Via Integration Quadratures[J].Numerische Mathematik,2005,100(1):141-163.
  • 6Salinetti G. Consistency of statistical estimators: the epigraphical view[G]//Uryasev S, Pardalos P M. Stochastic Optimization: Algorithms and Applications. Dordrecht: Kluwer Academic Publishers, 2001: 365-383.
  • 7Dupacova J, Wets R J B. Asymptotic behavior of statistical estimators and of optimal solutions of optimization problems[J]. The Annals of Statistics, 1988,16(4) : 1517-1549.
  • 8Artstein Z, Wets R J B. Consistency of minimizers and the SLLN for stochastic programs[J]. Journal Convex Analysis, 1995,2(1) : 1-17.
  • 9Hess C. Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator[J]. The Annals of Statistics, 1996,24 (4) : 1298-1315.
  • 10Pennanen T, Koivu M. Epi-convergent discretizations of stochastic programs via integration quadratures [J]. Numerische Mathematik, 2005,100(1) : 141-163.

引证文献2

数学学报（中文版）
2009年 第5期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部