一類不可微優(yōu)化算法及在線性分類問題中的應(yīng)用.pdf

1、西安科技大學碩士學位論文一類不可微優(yōu)化算法及在線性分類問題中的應(yīng)用姓名：鄭穎春申請學位級別：碩士專業(yè)：應(yīng)用數(shù)學指導教師：王雪峰20080415Subject：AClassofAlgorithmforNondiffenrentiableOptimizationandTheApplicationforLinearClassificationSpecialty：AppliedMathematicsName：ZhengYing—chunInst

2、ructor：WangXue—fengABSTRACT(Signature)j血粵顯孚縱(Signature)Thisthesisintroducesthenondiffenrentiableoptimizationtheoryandalgorithm，includinghistoryofthedevelopment，researchsignification，applicationareasandstudystatusquoPropo

3、setheconceptofcircumscribecuboidinthebicompactconvexsetandconstructacircumscribecuboidinasubdifferentiablesetOnthisbasisaclassofnondiffenrentiableoptimizationalgorithmisgiventosolvetheunconstrainedproblemnlealgorithmisdi

4、fferentfromthecurrentmethodsThesureforsearchdirectiondonotrequirecalculatesubdifferentiablesetandanyordersubgradient，andsolveanytwoorderprogrammingItsimplycomputes2ndirectionalderivativesneconvergenceofthealgorithmisalso

5、proofnlepaperprovesseveralintegralmediantheoremsandthelinearconvergenceofthealgorithmundercertainconditionsthroughtheintroductionoftheconceptofseconddirectionalderivativeForthecharacteristicsofmaxfunctiontheaccountofs—su

6、bgradientofmaxfunctionisgivenandthenaclassofalgorithmisgainedtoresolveaminimaxproblemandtheconvergenceofthealgorithmisproofBynumericalexperimentforthetwotypesoffuncfion，thenumericalresultsshowthatthegivenalgorithmisfeasi

7、bleandeffective，andhasthecharacteristicsoflargescaleconvergenceCompare、7Iriththeexistingnondiffenrentiableoptimizationalgorithm，ouralgorithmhastheadvantagesoffastconvergenceanditerativefewerEspeciallyforthefunctionprovid

8、ed、ⅣitllrigorousnondiffenrentiablepointandtheminimaxproblemouralgorithmhastheevenobviousadvantagesFinally，linearclassificationproblemsareconvertedtoaclassofunconstrainedoptimizationproblemAndthethesispresentanumericalmet

9、hodforcalculatesubgradient，thentosolvelinearclassificationproblemsbyuseofthesubgradientalgorithmExamplesshowthatthenondiffenrentiableoptimizationalgorithmforlinearregressionequationissimpleandpracticalKeywords：nondiffenr