一類大型稀疏無約束優(yōu)化的算法.pdf

1、大連理工大學碩士學位論文一類大型稀疏無約束優(yōu)化的算法姓名：李軍祥申請學位級別：碩士專業(yè)：運籌學與控制論指導教師：張宏偉20050614AClassofAlgorithmsforLargeScaleSparseUnconstrainedOptimizationAbstractThisdissertationstudiesaclassofseveralalgorithmsforsolvinglargescalesparseunconstra

2、inedoptimizationItsmainresultsmaybesummarizedasfollows；lInChapter4，asymmetrictriangularpartitionedsecantmethodforsolvinglargescalesparseunconstrainedoptimizationproblemsisconstructed，whichisacombinationofasecantmethodand

3、afinitedifferencemethod，anddependsonaconsistentpar—titionofthecolumnsofthelowertriangularpartoftheHessianmatrix；itreducesthenumberofgradientevaluationsrequiredbyPoweltandToint’Salgorithm(theindirectlowertriangularsubstit

4、utionalgorithm)byoneateveryiterativestepAqsuperlinearconvergenceresultandanrconvergencerateestimateshowthatthismethodhasgoodlocalconvergenceproperties，andwesharpenerrorestimatesandimproveKantorovichtypeanalysesforBroyden

5、’SalgorithmandSchubert’Salgorithm2InChapter5，anewmethodwithdirectpartitionedcolumnupdatesofcholeskyfactor—izationforsolvinglargescalesparseunconstrainedoptimizationproblemsisproposed，whi出dependsOnaconsistentpartitionofth

6、ecolumnsandcholeskyfactorizationoftheHessianmatrix，Thismethodemploysaninitialcholeskyfactorizationandpar—titionedcolumnsoftheapproximationHessianandthencorrectsthecorrespondingcolumnsofthediagonalfactorandlowertriangular

7、factordirectlyandsuccessivelyateachstepIterationsaregeneratedusingforwardandbackwardsubstitutionemployingtheupdatefactorizations，Aselfcorrectingpropertyaqsuperlinearconvergenceresultandanr—convergeneerateestimateshowthat

8、thismethodhasgoodlocalcon—vergenceproperties3，Chapter6providesnumericalexperimentsgivenbythealgorithmsinchapter4andchapter5Thenumericalresultsshowthat，forsolvingsomelargescalesparseunconstrainedoptimizationproblems，thetw

9、oalgorithmsareobviouslymoreeffectivethananyotheralgorithmscomparedwithinsomeaspects。KeyWords：algorithm；superlinearconvergence；numericalexample；unconstrainedop—timization；sparsity；finitedifference；substitution；secant；Hess