论文标题
基于样品的全球化分布在强大的优化方面优化
Globalized distributionally robust optimization based on samples
论文作者
论文摘要
众所周知，扰动数据集是强大优化（RO）建模的关键。分布鲁棒优化（DRO）是一种用于优化受概率分布不确定的随机参数的优化问题的方法。就扰动数据的信息而言，必须估计公式DRO模型中概率分布的适当支持集。在本文中，我们介绍了两个全球化的分布鲁棒优化（GDRO）模型，该模型根据数据选择一个核心集和一个包含核心集的样本空间，以平衡同时稳健性和保守主义的程度。保守主义的程度可以由随机参数与核心集的预期距离控制。在某些假设下，我们进一步将几种GDRO模型重新制定为可访问的半明确计划。此外，还提供了数值实验，显示了GDRO模型的最佳目标值与样品空间的大小与核心集之间的关系。
It is known that the set of perturbed data is key in robust optimization (RO) modelling. Distributionally robust optimization (DRO) is a methodology used for optimization problems affected by random parameters with uncertain probability distribution. In terms of the information of the perturbed data, it is essential to estimate an appropriate support set of the probability distribution in formulating DRO models. In this paper, we introduce two globalized distributionally robust optimization (GDRO) models which choose a core set based on data and a sample space containing the core set to balance the degree of robustness and conservatism at the same time. The degree of conservatism can be controlled by the expected distance of random parameters from the core set. Under some assumptions, we further reformulate several GDRO models into tractable semi-definite programs. In addition, numerical experiments are provided showing the relationship between the optimal objective values of the GDRO models and the size of the sample space and the core set.
