{"title":"无约束最优化","authors":"N. Tutkun","doi":"10.1017/9781108347976.004","DOIUrl":null,"url":null,"abstract":"1. We say x ∈ X is a local maximum of f on X if there is r > 0 such that f(x) ≥ f(y) for all y ∈ X ∩B(x, r). If the inequality is strict, then we have a strict local maximum. 2. We say x ∈ X is a local minimum of f on X if there is r > 0 such that f(x) ≤ f(y) for all y ∈ X ∩B(x, r). If the inequality is strict, then we have a strict local minimum. 3. We say x ∈ X is a global maximum of f on X if f(x) ≥ f(y) for all y ∈ X. If the inequality is strict, then we have a strict global maximum.","PeriodicalId":345765,"journal":{"name":"Optimization Concepts and Applications in Engineering","volume":"37 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Unconstrained Optimization\",\"authors\":\"N. Tutkun\",\"doi\":\"10.1017/9781108347976.004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"1. We say x ∈ X is a local maximum of f on X if there is r > 0 such that f(x) ≥ f(y) for all y ∈ X ∩B(x, r). If the inequality is strict, then we have a strict local maximum. 2. We say x ∈ X is a local minimum of f on X if there is r > 0 such that f(x) ≤ f(y) for all y ∈ X ∩B(x, r). If the inequality is strict, then we have a strict local minimum. 3. We say x ∈ X is a global maximum of f on X if f(x) ≥ f(y) for all y ∈ X. If the inequality is strict, then we have a strict global maximum.\",\"PeriodicalId\":345765,\"journal\":{\"name\":\"Optimization Concepts and Applications in Engineering\",\"volume\":\"37 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-06-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Optimization Concepts and Applications in Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/9781108347976.004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optimization Concepts and Applications in Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/9781108347976.004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
1. We say x ∈ X is a local maximum of f on X if there is r > 0 such that f(x) ≥ f(y) for all y ∈ X ∩B(x, r). If the inequality is strict, then we have a strict local maximum. 2. We say x ∈ X is a local minimum of f on X if there is r > 0 such that f(x) ≤ f(y) for all y ∈ X ∩B(x, r). If the inequality is strict, then we have a strict local minimum. 3. We say x ∈ X is a global maximum of f on X if f(x) ≥ f(y) for all y ∈ X. If the inequality is strict, then we have a strict global maximum.
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