基于bundle修正策略的非光滑约束优化算法分析

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1、STUDmSoNNONSMOOTHCONSTRAD叮EDoPTIMIZATIoNALGoRITHMSBASEDoNBUNDLEMODIFICATIoNSTRATEGYABSTRACTNonsmoothoptimizationasanimportantbranchoftheoptimizationre—search，notonlyhasimportanttheoreticalsignificance，butalsoiswidelyusedinfieldsofoptimalcontrol，engineeringdesignandimageprocessin

2、gect．Thecoreissueonnonsmoothoptimizationresearchisaimedatdesigningv撕OUSoffastandemcientnumericalmethods．Thisthesisstudiesnewnu—mericalalgorithmsforsolvingnonsmoothconstrainedoptimizationproblem—Sbycombiningthebundlemodificationstrategy，feasibledirectionmethod，phaseI-phaseIImetho

3、dandsubgradientaggregationtechnique．Firstly,afeasibledirectionalgorithmforsolvingnonsmoothconstrainedoptimizationproblemisproposedbydesigningasuitablenewbundlemodifi—cationstrategyandcombiningwiththeideaoffeasibledirectionmethod．Thealgorithmcangeneratefeasibleiterationpointsande

4、nsurethattheobjectivefunctionvalueismonotonicallynonincreasing．Whenthestabilitycenterisupdated，thebundlemodificationstrategyisexecuted，andthealgorithmwillgenerateauxiliaryiterationpointswhichdescendfasterorhavebetterfeasi—bilityasalternativestothecorrespondingpointsinbundle，aimi

5、ngatgettingabetterbundleset．Inaddition，globalconvergenceofthealgorithmisproven．Secondly,withthenumberofiterationsincreases，inordertoavoidtheIIInumericalcalculationdifficultiescausedbythegraduallyexpandingofthesearchdirectionfindingsub—problem，thisthesisputsforwardafeasibledi-rec

6、tionalgorithmwithsubgradientaggregationtechnique．Byintroducingthesubgradientaggregationtechnique，thealgorithmaggregatesthegradientsinbundleset，thusthenumberofconstraintsofthedirectionfindingsubproblemisgreatlyreduced，followedbysignificantreductionofthecomputation．Thealgorithmsti

7、llhasglobalconvergence．Onceagain，toovercometheweaknessoffeasibledirectionmethodwhichrequiresafeasibleinitialpoint，withcombinationoftheideaofphaseI-phaseIImethod，thisthesisfurtherworksonfeasibledirectionalgorithmtopromoteaphaseI-phaseIIalgorithmforsolvingnonsmoothconsignedoptimiz

8、ationproblem．Thealgorithmcanacceptinfeasibleini