{"title":"用量词消去法求解半定规划","authors":"H. Anai","doi":"10.1109/ACC.1998.688368","DOIUrl":null,"url":null,"abstract":"Several interesting control system design and analysis problems can be reduced to quantifier elimination (QE) problems. In this paper, we focus on semidefinite programming (SDP) problems, which are one of the generic linear matrix inequality (LMI) problems. We present a new symbolic method based on QE for the SDP problems and show some experiment by using existing QE package to demonstrate the capability of the method. Though currently this method is practically applicable to modest size problems which existing QE software can solve, it gives one exact solutions and enables one to deal with nonconvex as well as parametric cases. Moreover, in our scheme, the model or parameter uncertainties are easy to incorporate in the SDP problems.","PeriodicalId":364267,"journal":{"name":"Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"23","resultStr":"{\"title\":\"On solving semidefinite programming by quantifier elimination\",\"authors\":\"H. Anai\",\"doi\":\"10.1109/ACC.1998.688368\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Several interesting control system design and analysis problems can be reduced to quantifier elimination (QE) problems. In this paper, we focus on semidefinite programming (SDP) problems, which are one of the generic linear matrix inequality (LMI) problems. We present a new symbolic method based on QE for the SDP problems and show some experiment by using existing QE package to demonstrate the capability of the method. Though currently this method is practically applicable to modest size problems which existing QE software can solve, it gives one exact solutions and enables one to deal with nonconvex as well as parametric cases. Moreover, in our scheme, the model or parameter uncertainties are easy to incorporate in the SDP problems.\",\"PeriodicalId\":364267,\"journal\":{\"name\":\"Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)\",\"volume\":\"13 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-06-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"23\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ACC.1998.688368\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ACC.1998.688368","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On solving semidefinite programming by quantifier elimination
Several interesting control system design and analysis problems can be reduced to quantifier elimination (QE) problems. In this paper, we focus on semidefinite programming (SDP) problems, which are one of the generic linear matrix inequality (LMI) problems. We present a new symbolic method based on QE for the SDP problems and show some experiment by using existing QE package to demonstrate the capability of the method. Though currently this method is practically applicable to modest size problems which existing QE software can solve, it gives one exact solutions and enables one to deal with nonconvex as well as parametric cases. Moreover, in our scheme, the model or parameter uncertainties are easy to incorporate in the SDP problems.
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