{"title":"正齐次递增函数与正规集的对偶性","authors":"A. Rubinov, B. Glover","doi":"10.1051/RO/1998320201051","DOIUrl":null,"url":null,"abstract":"A nonlinear duality operation is defined for the class of increasing positively homogeneous functions defined on the positive orthant (including zero). This class of function and the associated class of normal sets are used extensively in Mathematical Economics. Various examples are provided along with a discussion of duality for a class of optimization problems involving increasing functions and normal sets.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"15 1","pages":"105-123"},"PeriodicalIF":1.8000,"publicationDate":"1998-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"41","resultStr":"{\"title\":\"Duality for increasing positively homogeneous functions and normal sets\",\"authors\":\"A. Rubinov, B. Glover\",\"doi\":\"10.1051/RO/1998320201051\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A nonlinear duality operation is defined for the class of increasing positively homogeneous functions defined on the positive orthant (including zero). This class of function and the associated class of normal sets are used extensively in Mathematical Economics. Various examples are provided along with a discussion of duality for a class of optimization problems involving increasing functions and normal sets.\",\"PeriodicalId\":54509,\"journal\":{\"name\":\"Rairo-Operations Research\",\"volume\":\"15 1\",\"pages\":\"105-123\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"1998-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"41\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rairo-Operations Research\",\"FirstCategoryId\":\"91\",\"ListUrlMain\":\"https://doi.org/10.1051/RO/1998320201051\",\"RegionNum\":4,\"RegionCategory\":\"管理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"OPERATIONS RESEARCH & MANAGEMENT SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rairo-Operations Research","FirstCategoryId":"91","ListUrlMain":"https://doi.org/10.1051/RO/1998320201051","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
Duality for increasing positively homogeneous functions and normal sets
A nonlinear duality operation is defined for the class of increasing positively homogeneous functions defined on the positive orthant (including zero). This class of function and the associated class of normal sets are used extensively in Mathematical Economics. Various examples are provided along with a discussion of duality for a class of optimization problems involving increasing functions and normal sets.
期刊介绍：
RAIRO-Operations Research is an international journal devoted to high-level pure and applied research on all aspects of operations research. All papers published in RAIRO-Operations Research are critically refereed according to international standards. Any paper will either be accepted (possibly with minor revisions) either submitted to another evaluation (after a major revision) or rejected. Every effort will be made by the Editorial Board to ensure a first answer concerning a submitted paper within three months, and a final decision in a period of time not exceeding six months.
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