{"title":"单调性约束控制问题的一个极大值原理","authors":"M. Hellwig","doi":"10.2139/ssrn.1101438","DOIUrl":null,"url":null,"abstract":"The paper develops a version of Pontryagin's maximum principle for optimal control problems with monotonicity constraints on control variables. Whereas the literature handles such constraints by imposing an assumption of piecewise smoothness on the control variable and treating the slope of this variable as a new control variable subject to a nonnegativity constraint, the paper obtains the maximum principle without such an additional assumption. The result is useful for studying incentive problems with hidden characteristics when the type set is a continuum and preferences satisfy a single-crossing constraint.","PeriodicalId":247961,"journal":{"name":"Max Planck Institute for Research on Collective Goods Research Paper Series","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2008-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"28","resultStr":"{\"title\":\"A Maximum Principle for Control Problems with Monotonicity Constraints\",\"authors\":\"M. Hellwig\",\"doi\":\"10.2139/ssrn.1101438\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper develops a version of Pontryagin's maximum principle for optimal control problems with monotonicity constraints on control variables. Whereas the literature handles such constraints by imposing an assumption of piecewise smoothness on the control variable and treating the slope of this variable as a new control variable subject to a nonnegativity constraint, the paper obtains the maximum principle without such an additional assumption. The result is useful for studying incentive problems with hidden characteristics when the type set is a continuum and preferences satisfy a single-crossing constraint.\",\"PeriodicalId\":247961,\"journal\":{\"name\":\"Max Planck Institute for Research on Collective Goods Research Paper Series\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"28\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Max Planck Institute for Research on Collective Goods Research Paper Series\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2139/ssrn.1101438\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Max Planck Institute for Research on Collective Goods Research Paper Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.1101438","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Maximum Principle for Control Problems with Monotonicity Constraints
The paper develops a version of Pontryagin's maximum principle for optimal control problems with monotonicity constraints on control variables. Whereas the literature handles such constraints by imposing an assumption of piecewise smoothness on the control variable and treating the slope of this variable as a new control variable subject to a nonnegativity constraint, the paper obtains the maximum principle without such an additional assumption. The result is useful for studying incentive problems with hidden characteristics when the type set is a continuum and preferences satisfy a single-crossing constraint.
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