[1]徐海文,孙黎明.一类半正定变分不等式的随机下降算法[J].南京师范大学学报(自然科学版),2017,40(01):6.[doi:10.3969/j.issn.1001-4616.2017.01.002]
　Xu Haiwen,Sun Liming.The Stochastic Descent Algorithm for a Kind ofSemidefinite Variational Inequality Problem[J].Journal of Nanjing Normal University(Natural Science Edition),2017,40(01):6.[doi:10.3969/j.issn.1001-4616.2017.01.002]
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一类半正定变分不等式的随机下降算法()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第40卷
期数:
2017年01期
页码:
6
栏目:
·数学与计算机科学·
出版日期:
2017-03-31

文章信息/Info

Title:
The Stochastic Descent Algorithm for a Kind ofSemidefinite Variational Inequality Problem
文章编号:
1001-4616(2017)01-0006-07
作者:
徐海文1; 孙黎明2
(1.中国民用航空飞行学院计算机学院,四川 广汉 618307)(2.南京审计大学理学院,江苏 南京211815)
Author(s):
Xu Haiwen1; Sun Liming2
(1.College of Computer Science and Technology,Civil Aviation Flight University of China,Guanghan 618307,China)(2.College of Science,Nanjing Audit University,Nanjing 211815,China)
关键词:
半正定变分不等式问题; 校正投影收缩算法; 随机下降算法; 依概率收敛
Keywords:
semidefinite variational inequality problem; correction projection and contraction algorithm; stochastic descent algorithm; probability convergence
分类号:
O221
DOI:
10.3969/j.issn.1001-4616.2017.01.002
文献标志码:
A
摘要:
校正投影收缩算法的下降量证明中多次使用了放大不等式,因此本文利用满足固定均值的随机数适当扩张步长,得到了一类半正定变分不等式问题的随机下降算法. 在适当的假设条件下,利用马尔可夫不等式和依概率收敛的性质,给出了随机下降算法的依概率收敛性证明. 通过一系列的数值试验验证了随机下降算法的有效性,并且表明了合理选择随机数的均值和方差可以提高随机下降算法的计算效率.
Abstract:
The amplification inequality is used for many times in the proof of drop function of correction projection and contraction algorithm,so we propose the stochastic descent algorithm for a class of semidifinite variational inequality problem through the random steplength extension with the random number series satisfying the Gaussian distribution or Uniform distribution and these random number series have a fixed mean. Subsequently,the probability convergence of stochastic descent algorithm is provided by the properties of Markov’s inequality and probability convergence under some suitable conditions. Finally,some numerical experiments show the effectiveness and efficiency of the stochastic descent algorithm,and reasonable selecting mean and variance of random number can improve the efficiency of the algorithm.

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备注/Memo

备注/Memo:
收稿日期:2016-10-16.
基金项目:国家自然科学基金(U1233105).
通讯联系人:徐海文,博士生,副教授,研究方向: 最优化理论与算法. E-mail:xuhaiwen_dream@163.com
更新日期/Last Update: 1900-01-01