{"title":"拟凹形多层规划问题","authors":"H. Sadeghi, M. Esmaeili","doi":"10.1142/S0217595921500263","DOIUrl":null,"url":null,"abstract":"Multilevel programming appears in many decision-making situations. Investigation of the main properties of quasiconcave multilevel programming (QCMP) problems, to date, is limited to bilevel programming (only two levels). In this paper, first, we present an extension of the properties of quasiconcave bilevel programming (QCBP) problems for the case when three levels exist. Then, by induction on [Formula: see text] (the number of levels), we prove the existence of an extreme point of the polyhedral constraint region that solves the QCMP problem under given conditions. Ultimately, a number of numerical examples are illustrated to verify the results.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Quasiconcave Multilevel Programming Problems\",\"authors\":\"H. Sadeghi, M. Esmaeili\",\"doi\":\"10.1142/S0217595921500263\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Multilevel programming appears in many decision-making situations. Investigation of the main properties of quasiconcave multilevel programming (QCMP) problems, to date, is limited to bilevel programming (only two levels). In this paper, first, we present an extension of the properties of quasiconcave bilevel programming (QCBP) problems for the case when three levels exist. Then, by induction on [Formula: see text] (the number of levels), we prove the existence of an extreme point of the polyhedral constraint region that solves the QCMP problem under given conditions. Ultimately, a number of numerical examples are illustrated to verify the results.\",\"PeriodicalId\":8478,\"journal\":{\"name\":\"Asia Pac. J. Oper. Res.\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asia Pac. J. Oper. Res.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/S0217595921500263\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asia Pac. J. Oper. Res.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/S0217595921500263","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Quasiconcave Multilevel Programming Problems
Multilevel programming appears in many decision-making situations. Investigation of the main properties of quasiconcave multilevel programming (QCMP) problems, to date, is limited to bilevel programming (only two levels). In this paper, first, we present an extension of the properties of quasiconcave bilevel programming (QCBP) problems for the case when three levels exist. Then, by induction on [Formula: see text] (the number of levels), we prove the existence of an extreme point of the polyhedral constraint region that solves the QCMP problem under given conditions. Ultimately, a number of numerical examples are illustrated to verify the results.
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