求解大規(guī)模非線性界約束優(yōu)化問題的兩個信賴域內(nèi)點方法.pdf

1、北京交通大學碩士學位論文求解大規(guī)模非線性界約束優(yōu)化問題的兩個信賴域內(nèi)點方法姓名：宮靜申請學位級別：碩士專業(yè)：運籌學與控制論指導教師：王周宏20080601|匕立鑾通太堂亟堂位i金塞一△墾曼!塞△g!ABSTRACTABSTRACT：Twointeriortrustregionmethodsforlargescalenonlinearminimizationsubjecttosimpleboundsareproposedinthispap

2、erTheboundconstrainedproblemistransformedintoaquadratictrustre西onmodelbyaffinescalingtransformationbasedonthefirstorderandsecond—orderoptimalconditionsoftheoriginalproblemThentheLMTIapproachandtheSTIapproachareproposed，w

3、hichexecuteasubspaceimplementationduringthecourseofconstructingandsolvingthequadraticmodelrespectivelyFortheLMTIapproach，thelimitedmemoryBFGSformulawhichinvolvesacompactrepresentationoftheBFGSmatrixisusedtoupdatetheappro

4、ximationofHessianmatrixⅥmilefortheSTIapproachweconstructatwodimensionalsubspaceandthensolvethetrustregionsubproblemonitdirectlyDuringtheiterationsthetrialstepistruncatedwhennecessaryinordertokeepthestrictfeasibilityofthe

5、iterationpointsItisshownthattheLMTIapproachandtheSTIapproachhaveglobalconvergencepropertiesundersomereasonableassumptionsandwillachievelocalquadraticconvergencerateundersomeevenstrongerconditionsSotheconvergencepropertie

6、softhesubspacetrustregionmethodsareasstrongasthoseofitsfullspaceversionComputationalresultsoftheapproachesshowthattheyaresuitableforlargescalenonlinearbound—constrainedproblemsandthenumberofiterationswillnotincreaserapid

7、lywiththescale—upoftheproblemsTheLMTlapproachoutperformstheSTIapproachonthewholeFormostofthetests，itCanconvergetotheoptimalsolutioninfeweriterationsBothapproachesCanbecompetitivewiththeLBFGS—Bmethodonsometestproblems，whi