万仲平,纪昌明,陈开周.求解单阶段随机规划的一种光滑逼近法[J].数学研究及应用,1997,17(4):565~569
求解单阶段随机规划的一种光滑逼近法
A Smooth Approximating Method for Solving Single Stage Stochastic Programming
  
DOI:10.3770/j.issn:1000-341X.1997.04.018
中文关键词:  单阶段随机规划  光滑逼近法  上图收敛法
英文关键词:single stage stochastic programming  smooth approximating method  epi convergence.
基金项目:国家自然科学基金和国家教委优秀年轻教师基金资助.
作者单位
万仲平 武汉水利电力大学 
纪昌明 武汉水利电力大学 
陈开周 西安电子科技大学 
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中文摘要:
      本文借助某种离散方式把单阶段随机规划问题转化为具有多个约束的确定性非线性规划,然后利用极大熵函数方法,把此确定性规划转化为只带简单约束的非线性规划,由此提出了求解这种随机规划的光滑逼近法,同时给出了该法的收敛性分析,较好地克服了因提高离散精度导致约束函数个数迅速增大所带来的求解困难.
英文摘要:
      A smooth approximating method for solving single stage stochastic programs is proposed, and the convergence concerning this method is simultaneously given. The original problem is changed into a determinate nonlinear programs with many constraints by means of some discretizing random variable way, and then the determinate problem is transformed into a nonlinear programs with only simple constraint making use of the maximum entropy principle. Thus difficulties of rapidly growing of the number of constraints due to increasing of the discretizing random variable precision will be overcomed.
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