简介：Inthispaper,wepresentasmoothingNewton-likemethodforsolvingnonlinearsystemsofequalitiesandinequalities.Byusingtheso-calledmaxfunction,wetransfertheinequalitiesintoasystemofsemismoothequalities.ThenasmoothingNewton-likemethodisproposedforsolvingthereformulatedsystem,whichonlyneedstosolveonesystemoflinearequationsandtoperformonelinesearchateachiteration.Theglobalandlocalquadraticconvergencearestudiedunderappropriateassumptions.Numericalexamplesshowthatthenewapproachiseffective.

简介：ThispaperdiscussestheglobalexistenceandquenchingofthesolutiontotheNewtonfiltrationequationwiththenonlinearboundarycondition.Theauthorsalsodiscusstheprofileofthequenchingsolutioninthequenchingtimeandobtainthequenchingrateofthequenchingsolution.

简介：InthispaperwediscusstheconvergenceofamodifiedNewton’smethodpresentedbyA.Ostrowski[1]andJ.F.Traub[2],whichhasquadraticconvergenceorderbutreducesoneevaluationofthederivativeateverytwostepscomparedwithNewton’smethod.Aconvergencetheoremisestablishedbyusingaweakconditiona≤3-2(21/2)andasharperrorestimateisgivenabouttheiterativesequence.

简介：AconicNewtonmethodisattractivebecauseitconvergestoalocalminimizzerrapidlyfromanysufficientlygoodinitialguess.However,itmaybeexpensivetosolvetheconicNewtonequationateachiterate.InthispaperweconsideraninexactconicNewtonmethod,whichsolvesthecouicNewtonequationoldyapproximatelyandinsonmunspecifiedmanner.Furthermore,weshowthatsuchmethodislocallyconvergentandcharacterizestheorderofconvergenceintermsoftherateofconvergenceoftherelativeresiduals.

简介：Recentexperiencehasshownthatinterior-pointmethodsusingalogbarrierapproacharefarsuperiortoclassicalsimplexmethodsforcomputingsolutionstolargeparametricquantileregressionproblems.Inmanylargeempiricalapplications,thedesignmatrixhasaverysparsestructure.Atypicalexampleistheclassicalfixed-effectmodelforpaneldatawheretheparametricdimensionofthemodelcanbequitelarge,butthenumberofnon-zeroelementsisquitesmall.AdoptingrecentdevelopmentsinsparselinearalgebraweintroduceamodifiedversionoftheFrisch-NewtonalgorithmforquantileregressiondescribedinPortnoyandKoenker[28].Thenewalgorithmsubstantiallyreducesthestorage(memory)requirementsandincreasescomputationalspeed.Themodifiedalgorithmalsofacilitatesthedevelopmentofnonparametricquantileregressionmethods.Thepseudodesignmatricesemployedinnonparametricquantileregressionsmoothingareinherentlysparseinboththefidelityandroughnesspenaltycomponents.ExploitingthesparsestructureoftheseproblemsopensupawholerangeofnewpossibilitiesformultivariatesmoothingonlargedatasetsviaANOVA-typedecompositionandpartiallinearmodels.

简介：从Newton运动学第二定律和Newton万有引力定律出发,导出Kepler行星绕日运动三定律.

简介：Inthispaper,aswitchingmethodforunconstrainedminimizationisproposed.ThemethodisbasedonthemodifiedBFGSmethodandthemodifiedSR1method.Theeigenvaluesandconditionnumbersofboththemodifiedupdatesareevaluatedandusedintheswitchingrule.WhentheconditionnumberofthemodifiedSR1updateissuperiortothemodifiedBFGSupdate,thestepintheproposedquasi-NewtonmethodisthemodifiedSR1step.OtherwisethestepisthemodifiedBFGSstep.Theefficiencyoftheproposedmethodistestedbynumericalexperimentsonsmall,mediumandlargescaleoptimization.Thenumericalresultsarereportedandanalyzedtoshowthesuperiorityoftheproposedmethod.

简介：Thispaperconsiderstheexistenceandasymptoticestimatesofglobalsolutionsandfinitetimeblowupoflocalsolutionofnon-Newtonfiltrationequationwithspecialmediumvoidofthefollowingform:{ut/|x|^2-△pu=u^q,(x,t)∈Ω×（0,T),u(x,t)=0,(x,t)∈ЭΩ×（0，T），u（x，0）=u0(x),u0(x)≥0,u0(x)全不等于0，where△pu=div(|△↓u|^p-2△↓u),ΩisasmoothboundeddomaininR^N(N≥3),0∈Ω,2

简介：WestudyhowtousetheSR1updatetorealizeminimizationmethodsforproblemswherethestorageiscritical.Wegiveanupdateformulawhichgeneratesmatricesusinginformationfromthelastmiterations.Thenumericaltestsshowthatthemethodisefficent.

简介：WeprovideconvergenceresultsanderrorestimatesforNewton-likemethodsingeneralizedBanachspaces.TheideaofageneralizednormisusedwhichisdefinedtobeamapfromalinearspaceintoapartiallyorderedBanachspace.Convergenceresultsanderrorestimatesareimprovedcomparedwiththerealnormtheory.

简介：首先用微分中值定理推出了Newton-Leibniz公式,同时也用Newton-Leibniz公式推出了三个微分中值定理,从而证明了微分中值定理与Newton-Leibniz公式可互相证明.

简介：Inthisstudy,weuseinexactnewtonmethodstofindsolutionsofnonlinear,nondifferenti-ableoperatorequationsonBanachspaceswithaconvergencestructure.ThistechniqueinvolvestheintroductionofageneralizednormasanoperatorfromalinearspaceintoapartiallyorderedBanachspace.Inthiswaythemetricpropertiesoftheexaminedproblemcanbeanalyzedmoreprecisely.Moreover,thisapproachallmvsustoderivefromthesametheorem,ontheonehand,semi-localresultsofKantorovich-type,andontheotherhand,globalresultsbasedonmono-tonicityconsiderations.Furthermore,iveshowthatspecialcasesofourresultsreducetothecorrespondingonesalreadyintheliterature.Finally>ourresultsareusedtosolveintegralequationsthatcannotbesolvedwithexistingmethods.

简介：在这篇论文，non-quasi-Newton“有用于非强迫的优化问题的不精确的线搜索的s家庭被学习。为non-quasi-Newton的一个新更改公式“sfamily被建议。如果，有任何一个Wolfe类型orArmijo类型线搜索的组成的算法全球性并且Q-superlinearly收敛，这被证明要最小化的功能hasLipschitz连续坡度。

简介：Inthispaper,thesupercouvergenceofaclassofWilson-likeelementsisconsidered,andasuperconvergentestimateofWilson-likeelementsisobtainedforstrongregularmeshes.

简介：基于Thiele连分式，重新建立了求解非线性方程的经典的Newton迭代公式．为了避免求导数运算，采用差商可以近似代替导数的办法，得到Newton迭代方法的几个变体并给出了其收敛的阶数．最后，数值实例证实了这些迭代格式是有效的．

简介：Inthispaperweimprovethetwoversionsofthetwo-sidedprojectedquasi-Newtonmethod-onewasproposedbyNocedal&Overtonin[1]andtheotherwasdiscussedinourpreviouspaper,byintroducingthreedifferentmeritfunctionstomakeinexactone-dimensionalsearches.Itisshownthattheseimprovedquasi-Newtonalgorithmshavegainedglobalconvergencepropertywhichisnotpossessedbytheoriginaltwoalgorithms.

简介：InthispaperwereportasparsetruncatedNewtonalgorithmforhandlinglarge-scalesimpleboundnonlinearconstrainedminimixationproblem.ThetruncatedNewtonmethodisusedtoupdatethevariableswithindicesoutsideoftheactiveset,whiletheprojectedgradientmethodisusedtoupdatetheactivevariables.Ateachiterativelevel,thesearchdirectionconsistsofthreeparts,oneofwhichisasubspacetruncatedNewtondirection,theothertwoaresubspacegradientandmodifiedgradientdirections.ThesubspacetruncatedNewtondirectionisobtainedbysolvingasparsesystemoflinearequations.Theglobalconvergenceandquadraticconvergencerateofthealgorithmareprovedandsomenumericaltestsaregiven.

简介：

简介：Fortheimprovedtwo-sidedprojectedquasi-Newtonalgorithms,whichwerepresentedinPartI,weproveinthispaperthattheyarelocallyone-steportwo-stepsuperlinearlyconvergent.Numericaltestsarereportedthereafter.ResultsbysolvingasetoftypicalproblemsselectedfromliteraturehavedemonstratedtheextremeimportanceofthesemodificationsinmakingNocedal&Overton’soriginalmethonpractical.Furthermore,theseresultsshowthattheimprovedalgoritnmsareverycompetitiveincomparisonwithsomehighlypraisedsequentialquadraticprogrammingmethods.

简介：我们在伪Euclidean空间Rmm+n与索引m。我们导出基本几何数量的飘移拉普拉斯算符并且在伪距离功能获得他们的卷估计。最后，我们以吝啬的弯曲或高斯地图的图象在次要的生长条件下面证明刚硬结果。