求解帶約束P-調(diào)和變分問題的一類最優(yōu)化數(shù)值算法及應(yīng)用.pdf

1、上海交通大學(xué)碩士學(xué)位論文求解帶約束P調(diào)和變分問題的一類最優(yōu)化數(shù)值算法及應(yīng)用姓名：楊潔莉申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：黃建國(guó)20050201iiAnoptimizationalgithmfthepharmonicproblemwithconstraintsitsapplicationAbstractManymathematicalmodelsarisingfromthefieldssuchasthedenoisingofcol

2、fulimagesienteddiffusionliquidcrystalscanbedescribedassomenonlinearvariationalproblemswithconstraints(harmonicmappings).Itisimptantintherespectsoftheypracticalapplicationstodeveloptheeticalanalysisnumericalsimulationfsuc

3、hproblems.Thethesiswillfocusonthealgithmdesignnumericalanalysisnumericalsimulationfthepharmonicproblemwithconstraintswhichisusefulinthedenoisingofcolfulimageskeepingbrightnessthedeterminationoftheequilibriumstateofliquid

4、crystals.Itisaminimizationproblemofenergyfunctionalofpharmonicmapconstrainedinthesets1S2S.ThetraditionalmethodconsistsinfirstobtainingthecrespondingHamiltonJacobiequationsthensolvingitbysomereasonablenonoscillatydifferen

5、ceschemesthecrucialstepistochoosethetimestepproperlysoastogetthedesiredcomputationalperfmance.Howeverthiswkisnoteasytocarryoutproperly.Inthisthesisweintendtousetheoptimizationmethodtosolvesuchproblemsindertoavoidtheafeme

6、ntioneddifficulty.Wefirsttransfertheiginalinfinitedimensionalconstrainedoptimizationproblemintoafinitedimensionalunconstrainedoptimizationproblembymeansofsomequadraturesfdoubleintegrals.Meanwhiletoensuretherationalityoft