A unified approach to inverse robust optimization problems

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Mathematical Methods of Operations Research Pub Date : 2024-02-22 DOI:10.1007/s00186-023-00844-x

引用次数: 0

Abstract

A variety of approaches has been developed to deal with uncertain optimization problems. Often, they start with a given set of uncertainties and then try to minimize the influence of these uncertainties. The reverse view is to first set a budget for the price one is willing to pay and then find the most robust solution. In this article, we aim to unify these inverse approaches to robustness. We provide a general problem definition and a proof of the existence of its solution. We study properties of this solution such as closedness, convexity, and boundedness. We also provide a comparison with existing robustness concepts such as the stability radius, the resilience radius, and the robust feasibility radius. We show that the general definition unifies these approaches. We conclude with an example that demonstrates the flexibility of the introduced concept.

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逆鲁棒性优化问题的统一方法

摘要已开发出多种方法来处理不确定的优化问题。通常，这些方法从一组给定的不确定性开始，然后试图将这些不确定性的影响降至最低。相反的观点是，首先设定一个愿意支付的价格预算，然后找到最稳健的解决方案。在本文中，我们旨在统一这些反向鲁棒性方法。我们给出了问题的一般定义，并证明了其解决方案的存在性。我们研究了这一解决方案的特性，如封闭性、凸性和有界性。我们还提供了与现有鲁棒性概念（如稳定性半径、弹性半径和鲁棒可行性半径）的比较。我们表明，一般定义统一了这些方法。最后，我们通过一个示例展示了所引入概念的灵活性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods of Operations Research 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This peer reviewed journal publishes original and high-quality articles on important mathematical and computational aspects of operations research, in particular in the areas of continuous and discrete mathematical optimization, stochastics, and game theory. Theoretically oriented papers are supposed to include explicit motivations of assumptions and results, while application oriented papers need to contain substantial mathematical contributions. Suggestions for algorithms should be accompanied with numerical evidence for their superiority over state-of-the-art methods. Articles must be of interest for a large audience in operations research, written in clear and correct English, and typeset in LaTeX. A special section contains invited tutorial papers on advanced mathematical or computational aspects of operations research, aiming at making such methodologies accessible for a wider audience. All papers are refereed. The emphasis is on originality, quality, and importance.