半無限規(guī)劃離散化問題超線性收斂的模松弛可行方向法.pdf

1、廣西大學碩士學位論文半無限規(guī)劃離散化問題超線性收斂的模松弛可行方向法姓名：徐慶娟申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：簡金寶20060426ASUPERLINEARLYCONVERGENTNoRMRELAXEDMETHoDoFFEASIBLEDIRECTIoNSFoRFINELYDISCRETIZEDPRoBLEMSFRoMSEMI—INFINITEPRoGRAMMINGABSTRACTInrecentyears，sinceSemi

2、—In矗niteProgramming(SIP)problemshavewideapplicationbackground，manyefbrtshavebeenmadeintheresearchesofSIPEspeciallysince1990s，theresearchofSIPhasmadeagreatdeVelopmentbothinalgorithmcheoryandperformingalgorithmManyauthorsp

3、roposedvariouse髓ctiveapproachestosolvethistypeofproblemsInparticular，themethodofdiscretizationisamongthesealgorithms，whichcanapproximateconstraintfhnc“onbymeansofprogressively6nerdiscretizationofanintervalofcontinuousvar

4、iableAccordingly，solvingSIPproblemcanbesubstitutedbys01vingtheDiscretizedSemi—In6nite(DSI)probIem，whichhasaamountofconstraintsAstoDSIproblem，someauthorssuitablychooseconstraintindicesateachiterationwhilepreserVingtheglob

5、alandlocalconvergence，whichmayleadtosubstantialcomputationalsaving0n七heo乞herhand，theMethodofFeaSibleDirections(MFD)isanimportantmethodforsolVinginequalityconstrainedoptimizationSincenormrelaxedme協(xié)odoffeasibIedirectionisp

6、resented，ithasbeenfurtherstudiedandappliedwidelyMoreover，itisshownthatthenorm—relaxedmethodoffeasibledirectionhasgoodconvergencespeedInthispaper，combiningthetechniqueofupdatingdiscretizationindexsetateachiter—ationandthe

7、ideaofthenorm—relaXedMFD，wepresentaalgorithmfors01vinginequalityconstraintedDSIproblemsfromSIPAteachiteration，theiterationpointisfeasibleandthemain$earchdirectioniscomputedbysolvingonlyonedirection矗ndingsubproblem，iejaqu

8、adraticprogramming，andsomeappropriateconstraintsarechosenteducethecomputationalcostAhigh—ordercorrectiondirectioncanbeobtainedbysolvinganotherquadraticsubproblemwithonlvequalicyconstraintsUndersuitableconditions，thepro—p

9、osedalgorithmisproVedtopossesstheglobalconvergenceandsuperlinearconVergenceFinally，someelementarynumericalexperimentsarereportedKEYWoRDS：semi—ininiteprogramming；normrelaxedmethodoffeasibledirec—tion；globalconVergence；sup