大規(guī)模非光滑優(yōu)化的信賴(lài)域算法.pdf

1、中國(guó)科學(xué)技術(shù)大學(xué)碩士學(xué)位論文大規(guī)模非光滑優(yōu)化的信賴(lài)域算法姓名：呂立波申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：運(yùn)籌學(xué)與控制論指導(dǎo)教師：侯定丕20050401AbstractIYustRegionMethodisarelativelynewakOl’ithmforNonlinearOptimizationThefinepropertiesofreliability，robustnessandstrongconvergenceenableTrustRegio

2、nMethodtoplayanimportantroleinthenumericaloptimizationWeintroducedthebasicstrategyofthismetta)dindealingwithsmoothoptimizationandtheconvergenceprop—ertiesintimfirstchapterThebackgroundofNonsmoothOptimizationnimportantcon

3、lponentofNonlinearOptimizationanditsapplicationstootherdisciplineswereshowninthesecondchapterMaintheoreticalresultsandtwosortsofnumerieMmethodswerebrieflyintroducedatthebeginningThenweconstructedatrustregionalgorithmforS

4、emi—infiniteMini—maxProblemswhichoccurwidelyinengineeringandeconomicsTheconvergencepropertieswereprovedandnumericalexperimentsresultsshowthealgorithmissatisfactoryIneveryiterationoftrustregionalgorithm)welnustsolveasocal

5、led2_rustRegionSubploblem，ie，minimizingaquadraticfunctionconstrainedinanellipsoidInthelargescalecsses，thissubproblemisquitedifficulttobesolvedbytheclassicalalgorithmsInthethirdchapter，wediscussedtheupdatingmethodandstruc

6、tureoftrustregionsubproblematfirstThenweintroducedaSequentialSubspaceMethodandanalyzedtheconvergenceresultsofthemethodbasedondifferentchoice0fthesubspaeesInspiredbytheaboveanalysisamodificationoftheSequentiMSubspaceMetho

7、dwanmadelwhichnotonlyprovidestheglobalconvergence，butalsodecreasesthenumberofmatrixvectorproductsFinallyweshowedsomenumericalresultswithcomparisonAttheendofthisthesis，weconcludedsolrlespecialfeaturesthattrustregionstrate