摘要
许多有重要价值的实际问题的数学模型为极小极大分布鲁棒优化模型,该类模型常存在的分布是不确定的,基于Hellinger距离散度,探讨了极小极大分布鲁棒优化问题的一个等价形式.基于Hellinger距离散度函数构造了不确定集;用测度变换的方法把一个关于分布的优化问题转化为关于似然比的凸优化问题;利用凸优化问题的对偶理论证明了内部极大化问题解的存在性;建立了内部极大化问题的等价形式.
Many important and practical problems can be modeled as minimax robust optimization problems,which often exist uncertainty distribution.This paper aims at studying minimax robust optimization problems based on Hellinger-distance divergence.First of all,ambiguous set of distribution P is constructed with Hellinger-distance divergence function.Secondly,by applying the change-of-measure technique,the inner maximization problem with respect to distribution Pis converted to a convex optimization problem with respect to likelihood ratio（LR）.Moreover,existence of solution of the inner maximization problem is proved using the duality theory.Finally,an equivalent form of the inner maximization problem is established.
出处
《辽宁师范大学学报（自然科学版）》
CAS
2016年第1期11-14,共4页
Journal of Liaoning Normal University:Natural Science Edition
基金
国家自然科学基金项目(11171138)
辽宁省教育厅高等学校科学研究一般项目(L2015291)
