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：伪--牛顿方程为解决非线性的方程或非强迫的优化问题的系统在quasi-Newtonmethods起了一个中央作用。相反，平底锅建议了一个新方程，并且当时，证明它具有第二份订单第一份订单传统，在某些近似意义。在这篇论文，我们做二个方程的归纳作为特殊情况包括他们。概括方程被分析，并且新更改从它被导出。象DFP一样新更改在一套标准测试问题的计算实验超过了traditionalDFP更改。

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

简介：Analgorithmforsolvingaclassofsmoothconvexprogrammingisgiven.Usingsmoothexactmultiplierpenaltyfunction,asmoothconvexprogrammingisminimizedtoaminimizingstronglyconvexfunctiononthecompactsetwasreduced.ThenthestronglyconvexfunctionwithaNewtonmethodonthegivencompactsetwasminimized.

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.

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简介：牛顿的重复为单个Toeplitz矩阵的组逆的计算被修改。在每次重复，重复矩阵被一个矩阵与一个低排水量等级接近。因为重复矩阵的排水量结构，涉及牛顿的重复的thematrix向量增加能高效地被做。我们证明修改牛顿重复的集中仍然是很快的。数字结果被介绍表明建议方法的快集中。

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.

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

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