{"title":"不变和等变阶连续向量格值算子的Hahn-Banach型定理和次微分及其在优化中的应用","authors":"A. Boccuto","doi":"10.2478/tmmp-2021-0010","DOIUrl":null,"url":null,"abstract":"Abstract We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group G of homomorphisms. As applications to optimization problems with both convex and linear constraints, we present some Farkas and Kuhn-Tucker-type results.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"78 1","pages":"139 - 156"},"PeriodicalIF":0.0000,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization\",\"authors\":\"A. Boccuto\",\"doi\":\"10.2478/tmmp-2021-0010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group G of homomorphisms. As applications to optimization problems with both convex and linear constraints, we present some Farkas and Kuhn-Tucker-type results.\",\"PeriodicalId\":38690,\"journal\":{\"name\":\"Tatra Mountains Mathematical Publications\",\"volume\":\"78 1\",\"pages\":\"139 - 156\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tatra Mountains Mathematical Publications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/tmmp-2021-0010\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tatra Mountains Mathematical Publications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/tmmp-2021-0010","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization
Abstract We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group G of homomorphisms. As applications to optimization problems with both convex and linear constraints, we present some Farkas and Kuhn-Tucker-type results.
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