復(fù)半定規(guī)劃及其在系統(tǒng)和控制理論中的應(yīng)用.pdf

1、上海交通大學(xué)碩士學(xué)位論文復(fù)半定規(guī)劃及其在系統(tǒng)和控制理論中的應(yīng)用姓名：王建宏申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：王曉敏20070101ComplexSeefiniteProgrammingitsApplicationinSystemControlTheyAbstractComplexSeefiniteProgrammingitsApplicationinSystemControlTheyAbstractOverthepastfewy

2、earsconvexoptimizationseefiniteprogramminginparticularhavecometoberecognizedasavaluabletoolfcontrolsystemanalysisdesign.Anumberofimptantproblemsinsystemcontroltheycanberefmulatedasseefiniteprogrammingproblemsi.e.minimiza

3、tionofalinearobjectivesubjecttolinearmatrixinequalityconstraints.Fromseefiniteprogrammingdualitytheyconditionsfinfeasibilityofthelinearmatrixinequalitysaswellasdualoptimizationproblemscanbefmulated.Thesedualproblemscanin

4、turnbereinterpretedincontrolsystemtheetictermsoftenyieldingnewresultsnewproofsfexistingresultsfromcontrolthey.Meoverthemostefficientalgithmsfconvexoptimizationsolvetheprimaldualproblemssimultaneously.Insightintothesystem

5、theeticmeaningofthedualproblemcantherefebeveryhelpfulindevelopingefficientalgithms.Inthispaperweproposetheuseofcomplexseefiniteprogrammingi.e.theextensionofseefiniteprogramminginwhichonereplacestherealsymmetricmatricesby

6、complexHermitianmatrices.Inthefirstchapterwesummarilyintroducethedevelopmentoflinearmatrixinequalityseefiniteprogrammingaswellasthemainachievementsofthisthesisaresummarized.Inthesecondchapterweextendtheresultsofseefinite

7、programmingtotheHermitiancomplexfm.BoththeweakstrongdualitytheiescrespondingtoLagrangeproblemsoptimalityconditionsareestableshed.Meoverweproposeaprimaldualcentralpathalgithmfthesolutionoflargescalecomplexseefiniteprogram

8、mingproblemsarisingincontrol.Sincecomplexseefiniteprogrammingisreducibletoseefiniteprogramming.Thepolynomialtimesolvabilityofseefiniteprogrammingsimpliesthatcomplexseefiniteprogrammingsarealsosolvableinpolynomialtime.Int