幾種確定性全局優(yōu)化方法.pdf

1、Yl100076單位代碼10476學(xué)號(hào)0401281004分類號(hào)002212獗氦鏹瓢先孳碩士學(xué)位論文幾種確定性全局優(yōu)化方法學(xué)科、專業(yè)：計(jì)算數(shù)學(xué)研究方向：最優(yōu)化理論及應(yīng)用申請(qǐng)學(xué)位類別：理學(xué)碩士申請(qǐng)人：顧敏娜指導(dǎo)教師：申培萍教授二oo七年五月AbstractGlobaloptimizationproblemshavebeenwidelyappliedtoscienceeconomicsandemginceringandtheyinclude

2、economicmodeling，fixedcharges，finance，networksandtransportation，databasesandchipdesign，imageprocessing，nuclearandmechanicaldesign，chemicalengineeringdesignandcontrolmolecularbiologyandenvironmentalengineeringHowever，sinc

3、ethereexistmultiplelocaloptimathatdigerfromtheglobalsolutionstudyingglobaloptimalsolutionhaschallengeextremelyBranchandboundalgorithmiscommonlyusedinglobaloptimization，butthereareseveralshortcomingssucha8lowcomputational

4、efficiencyInthispaper，efficientalgorithmsaregiventononconvexquadraticprograms，8amoflinearratiosprogramsandnonconvexquadraticprogramswithadditionalmultiplicativeconstraints，respectivelyTheseproblems8xeallhotordifficultspo

5、tsinglobaloptimazationThecontentsofthispaperareasfollows：First，anewdeterministicapproachisgivenfornonconvexquadraticproblemThisalgorithmfirstdecomposestheobjectivefunctionofit，thenarelaxationlinearprogrammingofquadraticp

6、roblemisgivenaccordingtoalinearunderestimatorofthecorrespondingobjectivefunctionInadditionaregiondeletingorreducingruleisusedtoacceleratetheconvergenceoftheproposedbranch—andboundalgorithmandincreasethecomputationaleffic

7、iencyThetheoreticalanalysisandnumericalcomputationshowsthattheproposedmethodisconvergentandefficientSecond，for8urnoflinearratiosproblemwithcoefficients，weakdualitytheoremofLagrangeduaHtyisusedtoobtainaseriesoflinearrelax

8、ationprogrammingproblems；ThenthissequenceoflinearrelaxationprogrammingproblemsmsolvedandtheirsolutionsareusedtoapproachtotheglobaloptimalsolutionoftheinitialproblemSothealgorithmonlyinvolvehowtosolvethelinearprogrammsNum