求解大规模非线性界约束优化问题的两个信赖域内点方法

《求解大规模非线性界约束优化问题的两个信赖域内点方法》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、北京交通大学硕士学位论文求解大规模非线性界约束优化问题的两个信赖域内点方法姓名：宫静申请学位级别：硕士专业：运筹学与控制论指导教师：王周宏20080601

2、匕立銮通太堂亟±堂位i金塞一△垦曼!塞△g!ABSTRACTABSTRACT：Twointeriortrustregionmethodsforlarge-scalenonlinearminimizationsubjecttosimpleboundsareproposedinthispaper．Thebound·constrainedproblemistransformedintoaquadratictrustre西on

3、modelbyaffinescalingtransformationbasedonthefirst-orderandsecond—orderoptimalconditionsoftheoriginalproblem．ThentheLMTIapproachandtheSTIapproachareproposed，whichexecuteasubspaceimplementationduringthecourseofconstructingandsolvingthequadraticmodelrespectively．FortheLMTIapproach，thelimited

4、memoryBFGSformula,whichinvolvesacompactrepresentationoftheBFGSmatrixisusedtoupdatetheapproximationofHessianmatrix．ⅥmilefortheSTIapproachweconstructatwo·dimensionalsubspaceandthensolvethetrustregionsubproblemonitdirectly．Duringtheiterationsthetrialstepistruncatedwhennecessaryinordertokeept

5、hestrictfeasibilityoftheiterationpoints．ItisshownthattheLMTIapproachandtheSTIapproachhaveglobalconvergencepropertiesundersomereasonableassumptionsandwillachievelocalquadraticconvergencerateundersomeevenstrongerconditions．Sotheconvergencepropertiesofthesubspacetrustregionmethodsareasstrong

6、asthoseofitsfull-spaceversion．Computationalresultsoftheapproachesshowthattheyaresuitableforlarge-scalenonlinearbound—constrainedproblemsandthenumberofiterationswillnotincreaserapidlywiththescale—upoftheproblems．TheLMTlapproachoutperformstheSTIapproachonthewhole．Formostofthetests，itCanconv

7、ergetotheoptimalsolutioninfeweriterations．BothapproachesCanbecompetitivewiththeL-BFGS—Bmethodonsometestproblems，whichprovestheirvalidity．KEYWORDS：bound—constrainedoptimization；large-scaleproblem；trustregionmethod；subspaceimplementation；affinescalingtransformation；quadraticmodel；interiorme

8、thodCLASSNO：0221．2学位论文版权使用授权书本学位论文作者完全了解北京交通大学有关保留、使用学位论文的规定。特授权北京交通大学可以将学位论文的全部或部分内容编入有关数据库进行检索，并采用影印、缩印或扫描等复制手段保存、汇编以供查阅和借阅。同意学校向国家有关部门或机构送交论文的复印件和磁盘。(保密的学位论文在解密后适用本授权说明)学位论文作者签名：留韵导师签名．王同之签字日期：≥叼g年b月与El签字日期：弘。2年6月3日独创性声明本人声明所呈交的学位论文是本人在导师指导下进行的研究工作和取得的研究成果，除了文中特别