简介:EllipticPDE-constrainedoptimalcontrolproblemswithL^1-controlcost(L^1-EOCP)areconsidered.TosolveL^1-EOCP,theprimal-dualactiveset(PDAS)method,whichisaspecialsemismoothNewton(SSN)method,usedtobeapriority.However,ingeneralsolvingNewtonequationsisexpensive.Motivatedbythesuccessofalternatingdirectionmethodofmultipliers(ADMM),weconsiderextendingtheADMMtoL^1-EOCP.TodiscretizeL^1-EOCP,thepiecewiselinearfiniteelement(FE)isconsidered.However,differentfromthefinitedimensionalL^1-norm,thediscretizedL^1-normdoesnothaveadecoupledform.Toovercomethisdifficulty,aneffectiveapproachisutilizingnodalquadratureformulastoapproximatelydiscretizetheL^1-normandL^2-norm.Itisprovedthattheseapproximationstepswillnotchangetheorderoferrorestimates.Tosolvethediscretizedproblem,aninexactheterogeneousADMM(ihADMM)isproposed.DifferentfromtheclassicalADMM,theihADMMadoptstwodifferentweightedinnerproductstodefinetheaugmentedLagrangianfunctionintwosubproblems,respectively.Benefitingfromsuchdifferentweightedtechniques,twosubproblemsofihADMMcanbeefficientlyimplemented.Furthermore,theoreticalresultsontheglobalconvergenceaswellastheiterationcomplexityresultso(1/k)forihADMMaregiven.Inordertoobtainmoreaccuratesolution,atwo-phasestrategyisalsopresented,inwhichtheprimal-dualactiveset(PDAS)methodisusedasapostprocessoroftheihADMM.Numericalresultsnotonlyconfirmerrorestimates,butalsoshowthattheihADMMandthetwo-phasestrategyarehighlyefficient.
简介:我们与州依赖者的到达和一般服务分发学习一个单个服务者的排队系统,或简单地M(n)/G/1/K,在服务器跟随一条N政策并且当系统是空的时,度多重假期的地方。我们用增补可变技术提供一个递归的算法数字地计算系统的静止队列长度分发。唯一的输入要求是服务时间分发的Laplace-Stieltjes变换,假期时间分发,和州依赖者的到达评价。算法的Thecomputational复杂性是O(K~3)。
简介:在这篇论文,我们与州依赖者的服务学习一个排队系统andstate依赖的假期,或简单地G/M(n)/1/K。因为服务率是州依赖者的,这个系统作为特殊情况与车站假期的各种各样的类型包括G/M/c和G/M/c/K队列。我们用增补可变技术提供一个递归的算法数字地计算系统的静止队列长度分发。唯一的输入要求是theLaplace-Stieltjes变换内部到达分发以及州依赖者的服务率和州依赖者的假期率。在一份随后的同伴报纸,我们与州依赖者的假期学习它的双systemM(n)/G/1/K队列。
简介:Thispaperconsidersadiscrete-timeGeo/G/1queueinamulti-phaseserviceenvironment,wherethesystemissubjecttodisastrousbreakdowns,causingallpresentcustomerstoleavethesystemsimultaneously.Atafailureepoch,theserverabandonstheserviceandthesystemundergoesarepairperiod.Afterthesystemisrepaired,itjumpstooperativephaseiwithprobabilityqi,i=1,2···,n.Usingthesupplementaryvariabletechnique,weobtainthedistributionforthestationaryqueuelengthatthearbitraryepoch,whicharethenusedforthecomputationofotherperformancemeasures.Inaddition,wederivetheexpectedlengthofacycletime,thegeneratingfunctionofthesojourntimeofanarbitrarycustomer,andthegeneratingfunctionoftheserver’sworkingtimeinacycle.Wealsogivetherelationshipbetweenthediscrete-timequeueingsystemtoitscontinuous-timecounterpart.Finally,someexamplesandnumericalresultsarepresented.
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