{"title":"混合约束集合优化问题的Karush-Kuhn-Tucker最优性条件和对偶性","authors":"L. Tung, T. Khai, P. T. Hung, P. Ngọc","doi":"10.23952/jano.1.2019.3.07","DOIUrl":null,"url":null,"abstract":"In this paper, we consider set optimization problems with mixed constraints. We first investigate necessary and sufficient Karush-Kuhn-Tucker optimality conditions for strict minimal solutions. Then, we formulate types of Mond-Weir and Wolfe dual problems and explore duality relations under convexity assumptions. Some examples are provided to illustrate our results.","PeriodicalId":205734,"journal":{"name":"Journal of Applied and Numerical Optimization","volume":"22 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Karush-Kuhn-Tucker optimality conditions and duality for set optimization problems with mixed constraints\",\"authors\":\"L. Tung, T. Khai, P. T. Hung, P. Ngọc\",\"doi\":\"10.23952/jano.1.2019.3.07\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider set optimization problems with mixed constraints. We first investigate necessary and sufficient Karush-Kuhn-Tucker optimality conditions for strict minimal solutions. Then, we formulate types of Mond-Weir and Wolfe dual problems and explore duality relations under convexity assumptions. Some examples are provided to illustrate our results.\",\"PeriodicalId\":205734,\"journal\":{\"name\":\"Journal of Applied and Numerical Optimization\",\"volume\":\"22 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied and Numerical Optimization\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.23952/jano.1.2019.3.07\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Numerical Optimization","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23952/jano.1.2019.3.07","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Karush-Kuhn-Tucker optimality conditions and duality for set optimization problems with mixed constraints
In this paper, we consider set optimization problems with mixed constraints. We first investigate necessary and sufficient Karush-Kuhn-Tucker optimality conditions for strict minimal solutions. Then, we formulate types of Mond-Weir and Wolfe dual problems and explore duality relations under convexity assumptions. Some examples are provided to illustrate our results.