数学优化
核密度估计
稳健优化
投资组合优化
概率密度函数
报童模式
随机规划
概率分布
数学
最优化问题
维数之咒
随机优化
经验分布函数
计算机科学
文件夹
财务
统计
估计员
供应链
政治学
法学
经济
出处
期刊:INFORMS journal on optimization
[Institute for Operations Research and the Management Sciences]
日期:2023-01-01
卷期号:5 (1): 68-91
被引量:1
标识
DOI:10.1287/ijoo.2022.0076
摘要
In this paper, a distributionally robust optimization model based on kernel density estimation (KDE) and mean entropic value-at-risk (EVaR) is proposed, where the ambiguity set is defined as a KDE-[Formula: see text]-divergence “ball” centered at the empirical distribution in the weighted KDE distribution function family, which is a finite-dimensional set. Instead of the joint probability distribution of the random vector, the one-dimensional probability distribution of the random loss function is approximated by the univariate weighted KDE for dimensionality reduction. Under the mild conditions of the kernel and [Formula: see text]-divergence function, the computationally tractable reformulation of the corresponding distributionally robust mean-EVaR optimization model is derived by Fenchel’s duality theory. Convergence of the optimal value and the solution set of the distributionally robust optimization problem based on KDE and mean-EVaR to those of the corresponding stochastic programming problem with the true distribution is proved. For some special cases, including portfolio selection, newsvendor problem, and linear two-stage stochastic programming problem, concrete tractable reformulations are given. Primary empirical test results for portfolio selection and project management problems show that the proposed model is promising. Funding: This work was funded by the National Natural Science Foundation of China [Grants 11971092 and 11571061] and the Fundamental Research Funds for the Central Universities [Grants DUT15RC(3)037 and DUT18RC(4)067].
科研通智能强力驱动
Strongly Powered by AbleSci AI