{"title":"Statistical inference of semidefinite programming with multiple parameters","authors":"Jiani Wang, Liwei Zhang","doi":"10.3934/JIMO.2019015","DOIUrl":null,"url":null,"abstract":"The parameters in the semidefinite programming problems generated by the average of a sample, may lead to the deviation of the optimal value and optimal solutions due to the uncertainty of the data. The statistical properties of estimates of the optimal value and the optimal solutions are given in this paper, when the estimated parameters are both in the objective function and in the constraints. This analysis is mainly based on the theory of the linear programming and the perturbation theory of the semidefinite programming.","PeriodicalId":16022,"journal":{"name":"Journal of Industrial and Management Optimization","volume":"16 1","pages":"1527-1538"},"PeriodicalIF":1.2000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Industrial and Management Optimization","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.3934/JIMO.2019015","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The parameters in the semidefinite programming problems generated by the average of a sample, may lead to the deviation of the optimal value and optimal solutions due to the uncertainty of the data. The statistical properties of estimates of the optimal value and the optimal solutions are given in this paper, when the estimated parameters are both in the objective function and in the constraints. This analysis is mainly based on the theory of the linear programming and the perturbation theory of the semidefinite programming.
期刊介绍：
JIMO is an international journal devoted to publishing peer-reviewed, high quality, original papers on the non-trivial interplay between numerical optimization methods and practically significant problems in industry or management so as to achieve superior design, planning and/or operation. Its objective is to promote collaboration between optimization specialists, industrial practitioners and management scientists so that important practical industrial and management problems can be addressed by the use of appropriate, recent advanced optimization techniques.
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