半定規(guī)劃的外梯度法研究.pdf

1、西安電子科技大學(xué)碩士學(xué)位論文半定規(guī)劃的外梯度法研究姓名：李蕊申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：劉紅衛(wèi)20100101AbstractComparedwithlinearprogramming，vectorisreplacedbymatrixandnon—negativityofvectorisreplacedbysemidefinitepropertyofmatrixinsemidefiniteprogrammingThus，S

2、emidefiniteprogrammingis8_rlextensionoflinearprogrammingTherearemanymethodsforsolvingsemidefiniteprogramming，inwhichtheinteriorpointmethodsarethemostsuccessfulMostinteriorpointmethodsforlinearprogramminghavebeengeneraliz

3、edtolinearsemidefiniteprogrammingSemidefiniteprogrammingisabranchofconvexoptimizationproblemImportantapplicationsofsemidefiniteprogrammingexistincombinatorialoptimization，approximationtheorysystemandcontroltheoryandmecha

4、nicalandelectricalengineeringInvestigatingsemidefiniteprogrammingisverysignificativebothintheoryandinpracticeInthispaper，semidefiniteprogrammingiseffectivelytransformedintoavariationalinequalityproblemAnimprovedextragrad

5、ientmethodisproposed血ensemidefiniteprogrammingisslovedFordetail，weconcludethemasfollows：Therelationsofsomeimportantoptimizationproblemsalesystematicallystudiedinthispapersuchaslinearprogramming，convexquadraticprogramming

6、，secondorderconeprogramming，semidefiniteprogrammingandpolynomialoptimizationproblemsWhensemidefiniteprogrammingsatisfiestheSlaterconditions，linealsemidefiniteprogrammingandQuadraticSemidefiniteProgrammingaletransformedin

7、tovariationalinequalityproblemsInthispaperanewstrategyforcomputingcorrectionstepsizeisproposedingeneralextra—gradientmethodFurthertheconvergenceofthenewalgorithmisprovedNumericalexperimentshowsthatthenewmethodiseffective