Andreas Löhne, D. Dörfler, Alexandra Rittmann, Benjamin Weißing
{"title":"Solving bilevel problems with polyhedral constraint set","authors":"Andreas Löhne, D. Dörfler, Alexandra Rittmann, Benjamin Weißing","doi":"10.23952/jano.1.2019.3.04","DOIUrl":null,"url":null,"abstract":". In this paper, we study the relationship between bilevel programmes and polyhedral projection problems. Extending a well-known result by F¨ul¨op, we show that solving a bilevel problem with polyhedral constraints is equivalent to optimise the upper level objective over certain facets of an associated polyhedral projection problem. Utilising this result, we show how solutions to such bilevel problems can be computed.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"321 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Numerical Optimization","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23952/jano.1.2019.3.04","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
. In this paper, we study the relationship between bilevel programmes and polyhedral projection problems. Extending a well-known result by F¨ul¨op, we show that solving a bilevel problem with polyhedral constraints is equivalent to optimise the upper level objective over certain facets of an associated polyhedral projection problem. Utilising this result, we show how solutions to such bilevel problems can be computed.