简介：（ｘ）？Ｓ．Ｉｆｇ（ｘ）＝０，Ｓ＊（ｘ）＝Ｓ＊．ＭｏｍｎｉｔＳ／０ａｎｄｎｉｔＳ（ｘ）２ｎｉｔＳ，ｎｉｔＳ（ｘ）／０．Ｈｅｌｌｃｅ（Ｓ（ｘ））＊＝Ｓ＊（ｘ）ｈａｓａｃｏｍｐａｃｔｃｏｎｖｅｘｂａｓｅ，ｄｅｎｏｔｅｄｂｙＡ，ａｎｄｔｈｅｃｏｍｐａｃｔｃｏｎｖｅｘｂａｓｅｏｆＱ＊ｉｓｄｅｎｏｔｅｄｂｙＢ．｛０｝＊＝Ｒｅ．ＬｅｔＣ＝｛ｘＥＲｅ：ＩＩｘｌｌ＝１｝．ＴｈｅｎＣｉｓａｃｏｍｐａｃｔｂａｓｅｏｆ｛０｝＊．Ｌｅｔｓｕｐｐｏｓｅｔｈａｔ（３ｄＯＥＲ＂）（ＶＰＥＶ＊＼｛０｝）（ＰＴｐ）＂（ｘ；ｄｏ）＜０，ｆｒｏｍＬｅｍｍａ２．３ｔｈｅｒｅｅｄｅｓｔｓａｄＥＲ＂ｔｏｇｅｔｈｅｒｗｉｔｈｂ＞０ｓｕｃｈｔｈａｔＩｎｐａｒｔｉｃｕｌａｒ，ｆｉｘｉｎｇＴＥＢａｎｄＡ６Ａ，ｓｅｔｔｉｎｇｐ￣（ＥＴ，ａｃ，￣）ＥＶ＊ｗｉｔｈＥ＞０ａｎｄｕｅＣ，ｗｅＩｎｄｅｅｄ，ｉｆｔｈｅｒｅｅｘｉｓｔｓａａｌＥ（０，６）ｓｕｃｈｔｈａｔｈ（ｘ＋ａ＇ｄ）／０，ｗｅｃａｎｃｈｏｏｓｅＦＩＥＣｓａｔｉｓｆｙｉｎｇＵ，＂ｈ（ｘ＋ａ＇ｄ）＞０．Ｉｎ（４），ｌｅｔｔｉｎｇＥ－０，ｉｔｆｏｌｌｏｗｓｔｈａｔＵ＂ｈ（ｘ＋ｒｓ＇ｄ）＜０，ｗｈ?

简介：为从Picard重复观点解决nonsmooth方程介绍概括牛顿方法，近似牛顿方法，和切开的方法的分析。Picard重复的弱Jacobian的半径的细节工作；概括Jacobian；为piecewise方程的概括牛顿方法。

简介：Inthispaper,thegeometricalmeaningoftwobasicoptimalityconditionsforaclassofcommoncasesinnonsnaoothprogrammingisexposed.Thusitmakesthecheckofoptimalityconditionsforthisclassofnonsmoothprogrammingproblemmucheasier.

简介：Inthispaper,wepresentasuccessivequadraticprogramming(SQP)methodforminimizingaclassofnonsmoothfunctions,whicharethesumofaconvexfunctionandanonsmoothcompositefunction.ThemethodgeneratesnewiterationsbyusingtheArmijo-typelinesearchtechniqueafterhavingfoundthesearchdirections.Globalconvergencepropertyisestablishedundermildassumptions.Numericalresultsarealsooffered.

简介：Inthispaper,weinvestigatetheoptimalityconditionsofaclassofspecialnonsmoothprogrammingminF(x)=∑mi=1|max{fi(x),ci}|whicharisesfromLl-normoptimization,whereci∈Risconstantandfi∈C^l,i=1,2,…,m.Theseconditionscaneasilybetestedbycomputer.

简介：Akindofnondecreasingsubgradientalgorithmwithappropriatestoppingrulehasbeenproposedfornonsmoothconstrainedminimizationproblem.Thedualtheoryisinvokedindealingwiththestoppingruleandgeneralglobalminimiizingalgorithmisemployedasasubroutineofthealgorithm.Themethodisexpectedtotacklealargeclassofnonsmoothconstrainedminimizationproblem.

简介：Inthispaper,wepresentanonmonotonealgorithmforsolvingnonsmoothcompositeoptimizationproblems.Theobjectivefunctionoftheseproblemsiscompositedbyanonsmoothconvexfunctionandadifferentiablefunction.Themethodgeneratesthesearchdirectionsbysolvingquadraticprogrammingsuccessively,andmakesuseofthenonmonotonelinesearchinsteadoftheusualArmijo-typelinesearch.Globalconvergenceisprovedunderstandardassumptions.Numericalresultsaregiven.

简介：Thispaperpresentsacoordinategradientdescentapproachforminimizingthesumofasmoothfunctionandanonseparableconvexfunction.Wefindasearchdirectionbysolvingasubproblemobtainedbyasecond-orderapproximationofthesmoothfunctionandaddingaseparableconvexfunction.UnderalocalLipschitzianerrorboundassumption,weshowthatthealgorithmpossessesglobalandlocallinearconvergenceproperties.Wealsogivesomenumericaltests(includingimagerecoveryexamples)toillustratetheefficiencyoftheproposedmethod.

简介：弱效率的条件为最小化其各个部件是可辨的功能的和的向量功能和凸的功能的问题被给的必要的Kuhn衣领类型，题目到在类似于Abadie限制资格的条件下面的ℝn,的凸的子集C上的一套可辨的非线性的不平等，或Kuhn衣领限制资格，或Arrow-Hurwicz-Uzawa限制资格。

简介：为解决抑制nonsmooth优化问题介绍一个不精确的信任区域算法。算法的全球集中；算法上的假设；在批评的点和静止的点之间的关系。

简介：Backlash-likehysteresisisoneofthenonsmoothandmulti-valuednonlinearitiesusuallyexistinginmechanicalsystems.Thetraditionalidentificationmethodisquitedifficulttobeusedtomodelthesystemsinvolvedwithsuchcomplexnonlinearities.Inthispaper,anonsmoothrecursiveidentificationalgorithmforthesystemswithbacklash-likehysteresisisproposed.Inthismethod,theconceptofClarkesubgradientisintroducedtoapproximatethegradientsatnonsmoothpointsandtheso-calledbundlemethodisusedtoobtaintheoptimizationsearchdirectioninnonsmoothcases.Then,arecursivealgorithmbasedontheideaofbundlemethodisdevelopedforparameterestimation.Afterthat,theconvergenceanalysisofthealgorithmisinvestigated.Finally,simulationresultstovalidatetheproposedmethodonasimulatedmechanicaltransmissionsystemarepresented.

简介：Inthispaper,nonsmoothunivex,nonsmoothquasiunivex,andnonsmoothpseudounivexfunctionsareintroduced.Byutilizingthesenewconcepts,sufficientoptimalityconditionsforaweaklyefficientsolutionofthenonsmoothmultiobjectiveprogrammingproblemareestablished.WeakandstrongdualitytheoremsarealsoderivedforMond-Weirtypemultiobjectivedualprograms.

简介：这份报纸认为nonsmooth是半无限的得最高分的战略局部地包含Lipschitzinvex的部分编程问题(SIMFP)工作。作者为SIMFP建立必要optimality条件。作者建立在SIMFP的SIMFP的一个最佳的解决方案和分级的Lagrange功能的僵绳点之间的关系。进一步，作者学习为SIMFP定义的向量Lagrange功能的僵绳点标准。

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