解非光滑優(yōu)化問題的光滑技術及理論.pdf

1、南京航空航天大學碩士學位論文解非光滑優(yōu)化問題的光滑技術及理論姓名：王傳芳申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：殷洪友20031201韭盞塑垡垡塑望墮簦鯊墨壟建——ABSTRACTFirstly，wewanttosolvetheproblemthatbasedonthebackgroundofsomenumericalproblemItisthespecialnondifferentiableoptimizationproblemWe

2、givetheoriginalproblemsometransform，thenwetrytofindtheparametricsmoothingapproximationsofthisnonsmoothfunctionWegivetheanalysisofthefundamentalmaximumfunction，bytwiceintegratingacorefunctionandfindfourtypesmoothingapprox

3、imationsforitthroughconvolution。WecontinuetofindthesmoothingapproximationsofgeneralmaximumfunctionAtlastweproposetheparametricsmoothingapproximationsoftheoriginalproblemWealsogivetheanalysisoftheerrorandtheresultofconver

4、genceThenewapproachtotheoriginalproblemisefficiencyandcorrectSowecanfreelychoosesomegoodsmoothoptimizationtechniquetodealwiththiskindnondlfferentiableoptimizationproblemSecondly，thenewgeneralizedgradientisintroducedtotak

5、eadvantageofthegivendirectionalderivativeWegivethedefinitionofthiSnewgeneralizedgradient，discussthepropertyandprovethemeanvaluetheoremAtthesametime，wecanobtainoptimalityconditionKeyword：NondifferentiableOptimization，Para