凸优化问题几类束方法对偶问题的-研究

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1、万方数据凸优化问题几类束方法对偶问题的研究forsolvingunconstrainedoptimizationproblems．whichlaysatheoreticalfoundationforthefurtherstudyofthesecondandthirdchapter．Thesecondchapter，wefirstlyintroducethegenerationandthebasicideaoftheproximalbundlemethod．Wemainlyuseoftheideaoftheproximalbundlemethodand

2、solvetheunconstrainedoriginalproblembytransformingitintoaseriesofquadraticprogrammingproblems．Fromtheviewpointofdualspaceweexplorethepenalizedsub．．problemsandprovesomeinterrelatedpropertiesbyadoptingdualspacetheory．Wealsoverifythattherelationshipbetweentheoriginalproblemanddual

3、problemandthespecificformsoftheoptimalsolutionofthesub—problemcanbeobtained，theexpressionofthesolutioniSsimilartothatinthepreviousarticles．Wesumuptherelationshipbetweentheoptimalsolutionofsub-problemandtheconvexcombinationofsubgradientsofpreviousiteratepoints，obtainthecorrespon

4、dingpropertiesofsubgradientsandthepredictiondescent．Secondly，theideaoftheproximalbundlemethodisappliedagain，andtheoptimizationproblemwithconstraintsistransformedintoanunconstrainedproblembyusingindicatorfunctions．Similarimportantconclusionsareobtainedatthesametime．Thethirdchapt

5、er，thedoublystabilizedbundlemethodisproposedanditsbasicideaisdescribed．Inthischapter，withthehelpoftheideasofproximalandlevelbundlemethod，wecoverttheoriginalproblemwithanon—smoothconvexobjectivefunctionandanon．emptyclosedconvexconstraintsettoaseriesofquadraticprogrammingproblems

6、withlevelconstraints．Andfurthermorewecoverttheconstrainedoptimizationproblemintoanunconstrainedoptimizationproblemsbyusingtheindicatorfunctionmethod．Next，similarlywecontinuetOfocusonthedoublystabilizedbundlemethod，fromtheviewpointofthedualproblem，wefindthedualproblemofthepenali

7、zedsub．problem，exploresomerelevantpropertiesinitsdualspaceandverifywhetherthespecificformsoftheoptimalsolutionofthesub-problemcanbeobtained，whethertherelationshipbetweentheoriginalproblemanddualproblemcanbedescribedlikeinchaptertwo．Finally，wesumuptherelationshipbetweentheoptima

8、lsolutionandtheconvexcombinationofsubgradientsofprevio