简介：Inthispaper,atrustregionmethodforequalityconstrainedoptlmizationbasedonnondiferentiableexactpenaltyisproposed.Inthisalgorithin,thetrailstepischaracterizedbycomputationofitsnormalcomponentbeingseparatedfromcomputationofitstangentialcomponent,i.e.,onlythetangentialcomponentofthetrailstepisconstrainedbytrustradiuswhilethenormalcomponentandtrailstepitselfhavenoconstraints.Theothermaincharacteristicofthealgorithmisthedecisionoftrustregionradius.Here,thedecisionoftrustregionradiususestheinformationofthegradientofobjectivefunctionandreducedHessian.However,Maratoseffectwilloccurwhenweusethenondifferentiableexactpenaltyfunctionasthemeritfunction.Inordertoobtainthesuperlinearconvergenceofthealgorithm,weusethetwiceordercorrectiontechnique.Becauseofthespecialityoftheadaptivetrustregionmethod,weusetwiceordercorrectionwhenp=0(thedefinitionisasinSection2)andthisisdifferentfromthetraditionaltrustregionmethodsforequalityconstrainedopthnization.Sothecomputationofthealgorithminthispaperisreduced.Whatismore,wecanprovethatthealgorithmisgloballyandsuperlinearlyconvergent.

简介：Thispaperpresentsatrustregionalgorithmwithnullspacetechniquefornonlinearequalityconstrainedoptimization.Consideringinthenullspacemethodsthat,theconvergentrateofrangespacestepisfasterthanthenullspacestepforthemostcases,theproposedalgorithmcomputesnullstepsmoreoftenthanrangespacestep.Moreover,thenewalgorithmisbasedonthereducedHessianSQPmethod.Globalconvergenceoftheproposedalgorithmisproved.Theeffectivenessofthemethodisdemonstratedbysomenumericalexamples.