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

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Burg entropy-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,证明了基于Burg entropy-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Burg entropy-散度函数的不确定概率约束优化问题的等价形式.

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 prob- lem based on Burg entropy-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.