全局優(yōu)化中的填充函數(shù)算法及應(yīng)用.pdf

1、上海大學(xué)碩士學(xué)位論文全局優(yōu)化中的填充函數(shù)算法及應(yīng)用姓名：安瀾申請學(xué)位級別：碩士專業(yè)：運(yùn)籌學(xué)與控制論指導(dǎo)教師：張連生200405012004年上海大學(xué)碩士學(xué)位論文IIAbstractGlobaloptimizationproblemscangenerallybedescribedas：fPl““，㈣、7stz∈Xwhere?！势Aisadedsionvariable，f(x)isanobjectivefunctionandxc鐘isafea

2、sibleregionParticularlyifX=Rn，thenproblem(P)iscalledunconstrainedopti—mizationOtherwise，ifXconsistsofbothequalityandinequalityconstraints，problem(P)iscalledconstrainedoptimizationThispaperonlydiscussestheoryandalgorithms

3、ofunconstrainedglobaloptimizationMethodsforsolvingglobaloptimizationareeffectivelyappliedinsciencetechnologyen百nearingdesign，economicsandmanagementResearchonglobaloptimizationhasmaderapidprogressforrecentdecadesManyschol

4、arshaveproposedvariousapproachesforglobaloptimizationAtpresent，therearemainlysuchmethodsasintervalmethod，integrallevelsetmethod，tunnelingfunctionmethod，filledfunctionmethodandSOonThefirsttwomethodshaverelativelybettercon

5、vergentpropertyandcriteriontodistin—guishglobalsolutionsHowever，itistoodimeulttoobtainglobalinformationasLipschitzconstant，uniformcontinuityconstant，boundedderivative，levelsetandetcOnthecon—trast，therearemoreefficientway

6、stodealwithlocalinformationSOthatlocalminimizerscanbeeasilyfoundThenbyconstructingauxiliaryfunctions，tunnelingfunctionmethodandfilledfunctionmethodareabletofindglobalsolutionsstepbystep，althoughtheyarelackofterminalcondi

7、tionThecoreinthispaperistoanalyzetheory，algorithmsandapplicationsofseveralfilledfunctionsFilledfunctionmethodwasfirstproposedbyRenpuGeFilledfunctionswithoneortwoparametershavebeenstudiedandappliedButbecausethoseparameter

8、saretoohardtobechosenitishighlypossiblethatglobaloptimizersarelostorfakebetterminimizersarefoundforsomefilledfunctionsThismotivatesastoanswertheproblemmentionedin[1】whetherparameterfreefilledfunctionexistsornotByhavingco

9、nstructedP(。，z)，wedefinitelyconcludethatparameterfreefilledfunctionexistsandnumericalexperimentsshowthealgorithmiseffectiveBasedonP(x，z)，wefurtherconstructcorrespondingfilledfunctionsP(x，z4，肛)，P(x，。，pP)andcomparethealgor

10、ithmofP(x。)withthatofP(x，礦，Ⅳ)Insection3，weimprovetheoriginaldefinitionoffilledfunctionNewfilledfunctionsarerequiredtohavelocalminimizersinsteadofbeingminimizedonthelinesegment，whichisveryimportantandmeaningfulteachagloba