简介：由Ginchev在我们证明足够、必要的optimality条件的那一些的这篇文章获得了，Guerraggio，Luc[Appl。数学，51，5鈥?6(2006)]概括(严格地)那些由Guerraggio介绍了，Luc[J。Optim。理论Appl，109，615鈥?29(2001)]。当以前的纸显示出在那里给的条件是有效的为例子时但是从后者纸的失败，它不通常证明那它建议的条件更强壮。在现在的笔记，我们与缺乏的证明完成这比较。关键词C1,1功能-概括秒顺序方向性的衍生物-Dini衍生物-弱有效的minimizer-秒顺序先生(2000)题目分类49K10的孤立的minimizer-49J52-49J50-90C29-90C30由捷克的管理(MSM6198959214)的委员会支持了

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简介：这篇论文为解决大规模学习一个替换secant/finite差别(SSFD)方法稀少的非强迫的优化问题。这个方法是一个正割方法和一个有限差别方法的联合，它取决于麻袋布矩阵的更低的三角形的部分的列的一个一致分区。q-superlinear集中结果和anr集中率估计证明这个方法有好本地集中性质。这个方法可能与一些是竞争的Thenumerical结果表演当前使用了算法。

简介：Thispaperpresentsatrustregiontwo-phasemodelalgorithmforsolvingtheequalityandboundconstratinednonlinearoptimizationproblem.Aconceptofsubstationarypointisgiven.Undersutableassumptions.theglobalconvergenceofthisalgorithmisprovedwithoutassumingthelinearindependenceofthegradientofactiveconstraints.Anumericalexampleisalsopresented.

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简介：Thispaperisconcernedwiththetopologicalstructureofefficientsetsforoptimizationproblemofset-valuedmapping.Itisprovedthatthesesetsareclosedorconnectedundersomeconditionsoncone-continuity,cone-convexityandcone-quasiconvexity.

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：在这篇论文，变光滑QP免费的不能实行的方法为非线性的不平等被建议抑制优化问题。这个反复的方法基于被获得由的非线性的方程的答案多钳子；为KKT一阶的optimality条件的变光滑的Fisher-Burmeister功能。与另外的QP免费的方法作比较，这个方法不请求重复的严格的可行性。特别地，这个方法是工具能；没有假定严格的补充条件全球性会聚；累积的孤立的海角指。而且，活跃限制的坡度没被请求线性地独立。初步的数字结果显示那这变光滑QP免费的不能实行的方法是相当有希望的。

简介：Somepropertiesofconvexconesareobtainedandareusedtoderiveseveralequivalentconditionsaswellasanotherimportantpropertyfornearlycone-subconvexlikeset-valuedfunctions.Undertheassumptionsofnearlycone-subconvexlikeness,aLagrangianmultipliertheoremonBensonproperefficiencyispresented.Relatedresultsaregeneralized.

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简介：Thealternatingdirectionmethodofmultipliers(ADMMforshort)isefficientforlinearlyconstrainedconvexoptimizationproblem.ThepracticalcomputationalcostofADMMdependsonthesub-problemsolvers.Theproximalpointalgorithmisacommonsub-problem-solver.However,theproximalparameterissensitiveintheproximalADMM.Inthispaper,weproposeahomotopy-basedproximallinearizedADMM,inwhichahomotopymethodisusedtosolvethesub-problemsateachiteration.Undersomesuitableconditions,theglobalconvergenceandtheconvergencerateofO(1/k)intheworstcaseoftheproposedmethodareproven.Somepreliminarynumericalresultsindicatethevalidityoftheproposedmethod.

简介：Basedonanewefficientidentificationtechniqueofactiveconstraintsintroducedinthispaper,anewsequentialsystemsoflinearequations(SSLE)algorithmgeneratingfeasibleiteratesisproposedforsolvingnonlinearoptimizationproblemswithinequalityconstraints.Inthispaper,weintroduceanewtechniqueforconstructingthesystemoflinearequations,whichrecurstoaperturbationforthegradientsoftheconstraintfunctions.Ateachiterationofthenewalgorithm,afeasibledescentdirectionisobtainedbysolvingonlyonesystemoflinearequationswithoutdoingconvexcombination.ToensuretheglobalconvergenceandavoidtheMaratoseffect,thealgorithmneedstosolvetwoadditionalreducedsystemsoflinearequationswiththesamecoefficientmatrixafterfiniteiterations.Theproposedalgorithmisprovedtobegloballyandsuperlinearlyconvergentundersomemildconditions.WhatdistinguishesthisalgorithmfromthepreviousfeasibleSSLEalgorithmsisthatanimprovingdirectionisobtainedeasilyandthecomputationcostofgeneratinganewiterateisreduced.Finally,apreliminaryimplementationhasbeentested.

简介：Thispaperstudiesthetwo-dimensionallayoutoptimizationproblem.Anoptimizationmodelwithperformanceconstraintsispresented.Thelayoutproblemispartitionedintofinitesubproblemsintermsofgraphtheory,insuchawayofthateachsubproblemovercomesitson-offnatureoptimalvariable.Aminimaxproblemisconstructedthatislocallyequivalenttoeachsubproblem.Byusingthisminimaxproblem,wepresenttheoptimalityfunctionforeverysubproblemandprovethatthefirstordernecessaryoptimalityconditionissatisfiedatapointifandonlyifthispointisazeroofoptimalityfunction.

简介：Inthispaper,westudyHenigefficiencyinvectoroptimizationwithnearlycone-subconvexlikeset-valuedfunction.TheexistenceofHenigefficientpointisprovedandcharacterizationofHenigefficiencyisestablishedusingthemethodofLagrangianmultiplier.Asaninterestingapplicationoftheresultsinthispaper,weestablishaLagrangemultipliertheoremforsuperefficiencyinvectoroptimizationwithnearlycone-subconvexlikeset-valuedfunction.

简介：在这篇论文我们在场为解决LC1的一个filter-trust-region算法使用第二Dini的非强迫的优化问题上面的方向性的衍生物。我们在合理假设下面建立算法的全球集中。

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

简介：Aclassoftrustregionmethodstorsolvinglinearinequalityconstrainedproblemsispropo6edinthispaper.Itisshownthatthealgorithmisofglobalconvergence.Thealgorithmusesaversionofthetwo-sldedprojectionandthestrategyoftheunconstrainedtrustregionmethods.Itkeepsthegoodconvergencepropertiesoftheunconstrainedcaseandhasthemeritsoftheprojectionmethod.Insomesense,ouralgorithmcanberegardedasanextensionandimprovementoftheprojectedtypealgorithm.

简介：InthispaperweprovethataclassoftrustregionmethodspresentedinpartⅠissuperlinearlyconvergent.Numericaltestsarereportedthereafter.Resultsbysolvingasetoftypicalproblemsselectedfromliteratureshavedemonstratedthatouralgorithmiseffective.