{"title":"一类非线性Schrödinger方程的最优控制问题的可解性","authors":"N. Yildirim Aksoy, E. Çelik, Muhammed Emin Dadas","doi":"10.11121/ijocta.2023.1371","DOIUrl":null,"url":null,"abstract":"In this paper, we analyze the solvability of the optimal control problem for a nonlinear Schr\\\"{o}dinger equation. A Lions-type functional is considered as the objective functional. First, it is shown that the optimal control problem has at least one solution. Later, the Frechet differentiability of the objective functional is proved and a formula is obtained for its gradient. Finally, a necessary optimality condition is derived.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"56 1","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The solvability of the optimal control problem for a nonlinear Schrödinger equation\",\"authors\":\"N. Yildirim Aksoy, E. Çelik, Muhammed Emin Dadas\",\"doi\":\"10.11121/ijocta.2023.1371\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we analyze the solvability of the optimal control problem for a nonlinear Schr\\\\\\\"{o}dinger equation. A Lions-type functional is considered as the objective functional. First, it is shown that the optimal control problem has at least one solution. Later, the Frechet differentiability of the objective functional is proved and a formula is obtained for its gradient. Finally, a necessary optimality condition is derived.\",\"PeriodicalId\":37369,\"journal\":{\"name\":\"International Journal of Optimization and Control: Theories and Applications\",\"volume\":\"56 1\",\"pages\":\"\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2023-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Optimization and Control: Theories and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11121/ijocta.2023.1371\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Optimization and Control: Theories and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11121/ijocta.2023.1371","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
The solvability of the optimal control problem for a nonlinear Schrödinger equation
In this paper, we analyze the solvability of the optimal control problem for a nonlinear Schr\"{o}dinger equation. A Lions-type functional is considered as the objective functional. First, it is shown that the optimal control problem has at least one solution. Later, the Frechet differentiability of the objective functional is proved and a formula is obtained for its gradient. Finally, a necessary optimality condition is derived.