计算数学    1994 16 (3): 333-346   ISSN: 0254-7791  CN: 11-2125/O1  

信赖域方法的收敛性
袁亚湘
中国科学院计算中心
收稿日期 null  修回日期 null  网络版发布日期 1994-03-14
参考文献  [1]J.V.Burke,ArobusttrustregionmethodforconstrainednonlinearprogrammingproblemsReportMCS-P131-0190,MathematicsandComputerScienceDivision,ArgonneNationalLaboratory,Argonne,Illinois,USA,1990[2]J.V.Burke,J.J.More,Ontheidentificationofactiveconstraints,SIAMJ.Numer.Anal,25(1988),1197-1211.[3]J.V.Burke,J.J.More;G.Toraldo,Conversencepropertiesoftrustregionmethodsforlinearandconvexconstraints,Math.Prog,(1990),305-336.[4]R.Byrd,R.B.Schnabel;G,AShultz;Atrustregionalsorithmfornonlinearlyconstrainedopti-mization,SIAMJournalofNumer.Anal,24(1987),1152-1170.[5]M.R.Celis,J.EDennis;R.A.Tapia,Atrustregionalgorithmfornonlinearequalityconstrainedoptimization,in:P.T.Boggs,R.H.ByrdandR.B.Schnabel,eds.;NumericalOptimization(SIAM,Philadelphia;1985),71-82[6]T.F.Coleman,A.R.Conn,Nonlinearprogrammingviaanexactpenaltyfunction:asymptoticanalysis,Math.Prog,24(1982),123-136.[7]A.R.Conn,N.I.M.Gould,Ph.L.Toint,Globalconvergenceofaclassoftrustregionalgorithmsforoptimizationwithsimplebounds;SIAMJ.NumerAnal,25(1988),433-460.[8]J.E.DennisH.H.W.Mei,Twonewunconstrainedoptimizationalgorithmswhichusefunctionandgradientvalues,J.Opt.TheoryandApplns,28(1979),453-482.[9]J.E.Dennis,J.J、MoreAcharacterizationofsuperlinearconvergenceanditsapplicationtoquasi-Newtonmethods,Math.Comp.;28(1974);549-560.[10]I.S.DuffJ.Nocedal,J.K.Rerd;Theuseoflinearprogrammingforthesolutionofsnarsesetsofnonlinearequations,SIAMJ.SciStat.Comput,8(1987);99-108.[11]M.EL-Alem,AglobalconvergencetheoryfortheCelis-Dennis-Tapiatrustregionalgorithmforconstrainedoptimization;Report;88-10,Math.SciencesDept,RiceUniversiltyTexas,USA,1988.[12]M.El-Hallabi,R.A.Tapia,Aglobalconvergencetheoryforarbitrarynormtrust-regionmethodsfornonlinearequations,TechnicalReport,87-25,Math.SciencesDept.,RiceUniversity,Texas,USA,1987.[13]R.Fletcher,PracticalMethodsofOptimization,Vol.1,UnconstrainedOptimization,JohnWileyandSons,Chichester,1980.[14]R.Fletcher,PracticalMethodsofOptimization,Vol.2,ConstrainedOptimization,JohnWileyandSoils,Chichester,1981.[15]R.Fletcher,AmodelalgorithmforcompositeNDOproblem,Math.Prog.Study,17(1982),67-76.(1982a)[16]R.Fletcher,Secondordercorrectionfornondifferentiableoptimization,in:G.A.Watson,ed.,NumericalAnalysis,Springer-Verlag,Berlill,1982,85-115.(1982b)[17]R.Fletcher,PracticalMethodsofOptimization(secondedition),JohnWileyandSons,Chichester,1987.[18]D.M.Gay,Computingoptimallocalconstrainedstep,SIAMJ.Sci.Stat.Comp.,2(1981)186-197.[19]D.M.Gay,Atrustregionapproachtolinearlyconstrainedoptimization,in:D.F.Griffiths,ed.,LectureNotesinMathematics1066:NumericalAnalysis,Springer-Verlag,Berlin,1984,72-105.[20]H.F.H.Khalfan,Topicsinquasi-Newtonmethodsforunconstrainedoptimization.PhDthesis,UniversityofColorado,1989.[21]K.Levenberg,Amethodforthesolutionofcertainnonlinearproblemsinleastsquares,Qart.Appl.Math.,2(1944),164-166.[22]N.Marotos,ExactPenaltyFunctionAlgorithmsforFiniteDimensionalandControlOptimizationProblems,Ph.D.thesis,ImperialCollegeSci.Tech.,UniversityofLondon,1978.[23]D.W.Marquardt,Analgorithmforleast-squaresestimationofnonlinearinequalities,SIAMJ.Appl.Math.,11(1963),431-441.[24]D.Q.Mayne,E.Polak,Asuperlinearlyconvergentalgorithmforconstrainedoptiminationprob-lems,Math.Prog.Study,16(1982),45-61.[25]J.J.More,TheLevenberg-Marquardtalgorithm:implementationandtheory,in:G.A.Watson,ed.,LectureNotesinMathematics630:NumericalAnalysis,Springer-Verlag,Berlin,1978,105-116.[26]J.J.More,Recentdevelopmentsinalgorithmsandsoftwarefortrustregionmethods,in:A.Bachem,M.GrstschelandB.Korte,eds.,Math.Prog.:TheStateoftheArt,Springer-Verlag,Berlin,1983,258-287.[27]J.J.More,Trustregionandprojectedgradients,ReportANL/MCS-TM-107,MathematicsandComputerScienceDivision,ArgonneNationalLaboratory,Argonne,Illinois,USA,1988.[28]J.J.More,D.C.Sorensen,Computingatrustregionstep,SIAMJ.Sci.Stat.Comp.,4(1983),553-572.[29]J.Nocedal,Y.Yuan,Combiningtrustregionandlinesearchtechniques,TechnicalReport,NAM06,DeptofComputerScience,NorthwesternUniversity,Illinois,USA,1991.[30]E.O.Omojokun,TrustRegionAlgorithmsforOptimizationwithNonlinearEqualityandInequal-ityConstraints,Ph.D.Thesis,UniversityofColoradoatBoulder,1989.[31]M.J.D.Powell,Anewalgorithmforunconstrainedoptimization,in:J.B.Rosen,O.L.MangasarianandK.Ritter,eds.,NonlinearProgramming,AcademicPress,NewYork,1970,31-66.[32]M.J.D.Powell,Convergencepropertiesofaclassofminimizationalgorithms,in:O.L.Mangasarian,R.R.MeyerandS.M.Robinson,eds.,NonlinearProgramming2,AcademicPress,NewYork,1975,1-27.[33]M.J.D.Powell,Ontheglobalconvergenceoftrustregionalgorithmsforunconstrainedoptimization,Math.Prog.,29(1984),297-303.[34]M.J.D.Powell,Y.Yuan,Atrustregionalgorithmforequalityconstrainedoptidrization,Math.Prog.,49(1991),189-211.[35]G.A.Shultz,R.B.Schnabel,R.H.Byrd,Afamilyoftrust-region-basedalgorithmsforunconstrainedminimizationwithstrongglobalconvergence,SIAMJ.Numer.Anal.,22(1985),47-67.[36]D.C.Sorensen,NeWton'smethodwithamodeltrustregionmodification,SIAMJ.Numer.Anal.,20(1982),409-426.(1982a)[37]D.C.Sorensen,Trustreginmethodsforunconstrainedoptimization,in:M.J.D.Powell,ed.,NonlinearOptimization1981,AcademicPress,London,1982,29-38.(1982b)[38]T.Steihaug,Theconjugategradientmethodandtrustregionsinlargescaleoptimization,SIAMJ.Numer.Anal.,20(1983),626-637.[39]S.W.Thomas,Sequeotialestimationtechniquesforquasi-Newtonalgorithms,Report,75-227,DeptofComputerScience,CornellUniversity,Ithaca,NY,USA,1975.[40]Ph.L.Toint,Global,convergenceofaclassoftrustregionmethodsfornonconvexminimizationinHilbertspace,IMAJ.Numer.Anal.,8(1988),231-252.[41]A.Vardi,Atrustregionalgorithmforequalityconstrainedminimization:convergencepropertiesandimplementation,SIAMJ.Numer.Anal.,22(1985),575-591.[42]R.S.Womersley,Localpropertiesofalgorithmsforminimizingnonsmoothcompositefunctions,Math.Prog.,32(1985),69-89.[43]Y.Yuan,Anexampleofonlylinearlyconvergenceoftrustregionalgorithmsfornonsmoothoptimization,IMAJ.Numer.Anal.,4(1984),327-335.[44]Y.Yuan,Conditionsforconvergenceoftrustregionalgorithmsfornonsmoothoptimization,Math.Prog.,31(1985),220-228.(1985a)[45]Y.Yuan,Onthesuperlinearconvergenceofatrustregionalgorithmfornonsmoothoptimization,Math.Prog.,31(1985),269-285.(1985b)[46]Y.Yuan,Onasubproblemoftrustregionalgorithmforconstrainedoptimisation,Math.Prog.,47(1990),53-63.[47]Y.Yuan,Adualalgorithmforminimizingaquadraticfunctionwithtwoquadraticconstraints,J.Comput.Math.,9(1991),348-359.[48]Y.Yuan,Anewtrustregionalgorithmfornonlinearoptimisationin:D.BainovandV.Covachev,eds.Proc.FirstInt.Col.Numer.Anal.,VSP,Zeist,1993,141-152.[49]Y.Yuan,Localconvergenceandnumericalresultsofatrustregionalgorithm,Report435,InstitutefurAngew.Math.,UniversityofWurzburg,Germany1993.[50]Y.Zhang,ComputingaCelis-Dennis-Tapiatrustregionstepequalityconstrainedoptimization,Math.Prog.,55(1992),109-124.

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