非凸半定規(guī)劃最優(yōu)性條件與增廣Lagrange方法.pdf

1、大連理工大學(xué)碩士學(xué)位論文非凸半定規(guī)劃最優(yōu)性條件與增廣Lagrange方法姓名：李潔申請(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：張立衛(wèi)20060610非凸半定規(guī)劃最優(yōu)性條件與增廣Lagrange方法optimalityConditionsforNonconVexSemide最niteProgr踟mingaIldAug瑚【entedLagrangianMethodAbstractThisdissertationisdeVotedtodi

2、8cussiⅡgtheopnmalityconditionsanda皿alyzingtheaugmentedLagran西anmethodfornoncoⅡvexsemide脅teprogr㈣ingThemaiⅡcontents，inthisdjssertation，maybesummarized明foHdws：1Chapter2，mainlysuInm盯izingtheopt血antycondition8forthenonconvex

3、semidefiⅡiteprogramming，flrstrec址18theconceptoftransver8alitycondition，provesthattra丑sVersalityconditionand1bearind印endencecond讓bnareeql】iv缸e11t，andshoⅣsthatunderstrictcomplementaritycondition，thetransvers曲tyconditionisa

4、su伍一cientconditionforuniquenessoftheLagrangemultipliersBasedonthepropertiesofcon8traint8etofnonconvexsernjde6血teprogr跚血ng，wederiveaconcretee沖ressionforconstra砒set’sfir8tordertangentconeand8econd—ordertangentset，鋤de8tabⅡs

5、htheoptimautyconditionsfornoⅡcollvex8鋤ide且niteprogrammi工19undersome臼ssumptiOns2Ch印ter3，beingthemainpartofthjsdissertation，comrertsnonconveXsemidefiniteprogr鋤mingproblem(sDP)tononlinearpmgr鋤mingproblem(ESDP)，andprovesthat

6、undertran8versalitycondition，strictcomplementarityconmtionandthesⅢ丑cientoptimalityconditionof10cals01utions，(sDP)and(EsDP)areequivment10callvMoreover，wepresen七acollVergencetheoremoftheaugrIleⅡtedLagrangianmethodforthenon

7、linearprogr蛐聊_ingproblem(EsDP)ThecoⅡvergencetheoremshoWsthattheaugmentedLagran酉anmethodi8locallyconwrgentwhenthepenal夠parametercisgreaterthanathresh01dandtheerrorboundofprimal一dual80lutionsisproportionaltoc一1KeyWords：Non