{"title":"逆鲁棒性优化问题的统一方法","authors":"","doi":"10.1007/s00186-023-00844-x","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>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.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"18 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A unified approach to inverse robust optimization problems\",\"authors\":\"\",\"doi\":\"10.1007/s00186-023-00844-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3>Abstract</h3> <p>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.</p>\",\"PeriodicalId\":49862,\"journal\":{\"name\":\"Mathematical Methods of Operations Research\",\"volume\":\"18 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-02-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Methods of Operations Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00186-023-00844-x\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods of Operations Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00186-023-00844-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A unified approach to inverse robust optimization problems
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.
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.