文章摘要
任咏红,赵得利,顾 钰.基于Burg entropy-散度函数的不确定概率约束优化问题的等价形式[J].海南师范大学学报自科版,2016,29(1):1-5
基于Burg entropy-散度函数的不确定概率约束优化问题的等价形式
An Equivalent Form of Ambiguous Probabilistic Constrained Optimization Problem Based on Burg Entropy-divergence Function
投稿时间:2015-09-13  修订日期:2016-03-01
DOI:10.12051/hainansfxyxb.2016.01.001
中文关键词: Burg entropy-散度函数  似然比  不确定概率约束优化  测度变换
英文关键词: Burg entropy-divergence  likelihood ratio  ambiguous probabilistic constrained optimization  change-of-measure technique
基金项目:国家自然科学基金面上项目(11171138);辽宁省教育厅科学研究一般项目(L2015291)
作者单位
任咏红 辽宁师范大学数学学院辽宁大连116029 
赵得利 辽宁师范大学数学学院辽宁大连116029 
顾 钰 辽宁师范大学数学学院辽宁大连116029 
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中文摘要:
      许多有重要价值的实际问题的数学模型均为概率优化模型,如水库系统设计问题、现金匹配问题等,该类模型通常存在分布的不确定性. 文章对概率优化模型的分布不确定性展开研究,探讨了基于Burg entropy-散度函数的不确定概率约束优化问题的一个等价形式. 构造了基于Burgentropy-散度函数的不确定集,用测度变换的方法把一个关于分布P的优化问题转化为关于似然比的凸优化问题,证明了基Burgentropy-散度函数的不确定概率约束优化问题解的存在性,并且得到了基于Burgentropy-散度函数的不确定概率约束优化问题的等价形式.
英文摘要:
      Many practical problems with important values can be modeled as probabilistic optimization problems, such as reservoir system design, cash matching, and so on, in which often exists distribution of uncertainty. This paper facuses on the uncertainty distribution, and aims at studying an equivalent form of ambiguous probabilistic constrained optimization problem based on Burgentropy-divergence function. Ambiguous set based on Burg entropy-divergence is constructed. With the change-of-measure technique, the optimization problem with respect to distribution P is converted to a convex optimization with respect to likelihood ratio. Existence of solutions of ambiguous probabilistic constrained optimization problem is proved based on Burg entropy-divergence function. Consequently, we obtain the equivalent form of ambiguous probabilistic con⁃ strained optimization problem based on Burg entropy-divergence function.
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