一個新的u-Lagrange函數(shù).pdf

1、大連理工大學碩士學位論文一個新的uLagrange函數(shù)姓名：于桂花申請學位級別：碩士專業(yè)：運籌學與控制論指導教師：張立衛(wèi)20060610一個新的甜_Lagrange函數(shù)ANEW甜一LAGRANGIANAbstractInnonsmoothopti工Ilization，thestudyconcerningthetheoryand印plicationofsecond—orderanaly8i8ofnonsmoothfunctionhasbe

2、enpaidmuchattentionLemar6chal，Mimin，Saga8tiz矗bal讎dOu8try(2000)【4】introducedthe甜V—decompositiontheomwhichopensawaytodefininga8uitablerestrictedsecond—orderderiV扯iveofacoIⅣeXfunction，atnondi趕、erentiablepoin骨Thebasisideai8t

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4、d，called“Lagran西an，ⅥatheLagrangian，itisp08sibleto矗nd8moothtrajectoriesa血dthesecond—ordere)幣ansionof，IntMsdis8erta土ion，weproposeanew“一Lagr齜19ian，studyingitspropertiesandapplicationsThecontentcanbesunlmafized：1Inchaper1，we

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6、comp。sitionSomebasicpropertiesofthe“一Lagran西anarepresentedThesere8ultscanhelpustodeeplyunderstandthefirstandsecond_orderexpansionof，onthe“一spaceF1lrthe皿ore，the“V—decompositionisappliedtoNLP：thetheoryonthepenaltyfunctiono

7、fconstrainedⅡliIliⅡlizationwithafinitenuIll_berofcon8tra主ntsaregeneraHzed3Inch印er3，aneW“一LagrangianisintrodueedWbdiscussthepropert主esofthenewfⅥnction(吼lcha呂the缶stIorder，higher—order阻dthesubdifferentialproperties)when7L白，

8、(孟)。dsts，thesecond—orderexpandsion。f，出ong牙0w()canbeabt8j玎ed4Inchaper4，weestablishtherelationbetweenthefunctionfanditstheMoreau—YosidaregularizationWealsodisscussthe8uf王icientandnecess盯vconditollsforthee)d8teneeofthe“一Hes

9、8ianBasingontheproposed甜V—theory，aconceptualsuplinearcoIlvergent甜gorithmcanbeusedtominimizeaconvexfunction，Wb出soc01lstnlctanalgorithmformillimizingitsMoreau—Yosidaregularization，becansethisisasmoothcorⅣexop伯nizationprobl