χ2-散度信息集下的分布鲁棒优化问题
A class of distributionally robust optimization problem under the distribution set controlled by χ2-distance
丁可伟 1刘玲伶2
作者信息
- 1. 西南民族大学数学学院,四川 成都 610041
- 2. 西南石油大学理学院,四川 成都 610500
- 折叠
摘要
讨论了χ2-散度刻画的信息集下的一类分布鲁棒优化问题.利用测度转换技巧及凸分析理论,得到该分布鲁棒优化问题的确定等价形式,其结构为经验分布下目标函数的期望添加了关于模糊因子和标准乘积的罚项.发现χ2-散度下的机会约束问题可以转化为经验分布下的更为保守的机会约束问题.最后讨论了一个χ2-散度信息集下的分布鲁棒投资组合问题并得到了其解析解.
Abstract
The distrubtionally robust optimization problem under the distribution set which is controlled by χ2-divergence was discussed.By the change-of-measure technique and convex analysis,the determinate equivalent form was obtained for the dis-trubtionally robust optimization problem.Then,it was found that the corresponding distributionally robust chance constrained problem could be transformed into the conservative chance constrained problem under the empirical probability measure.Final-ly,the closed form solution was obtained for distributionally robust portfolio problem.
关键词
分布鲁棒/机会约束/χ2-散度Key words
distributionally robust/chance constraint/χ2-distance引用本文复制引用
基金项目
中央高校基本科研业务费专项项目(2021128)
四川省自然科学基金青年基金项目(2022NSFSC1834)
出版年
2024
NETL
NSTL
万方数据