最优化方法与供应链信息管理中若干问题的研究

湖南大学硕士学位论文最优化方法与供应链信息管理中若干问题的研究姓名：赵沛桢申请学位级别：硕士专业：计算数学指导教师：李董辉20050420-I-IBFGSNewtonBFGSToint1981BFGSHessianToint1982Wolfe-PowellToint1986Li-Fukushima2001BFGSMBFGSBFGSHessianHessianHessianToint1986BFGSEDIEDIVANEDIInternetEDIInternetMailStandardICWed-EDIXML/EDIEDI2121MBFGSInternetEDI-II-AbstractAmongthequasi-Newtonmethodsforsolvingunconstrainedoptimizationproblemsinnumericalresult,theBFGSalgorithmconstitutesaparticularlyimportantclass.Thismethodconvergesgloballyandlocallyverywell.BecauseofthedensityofthematricesproducedbytheBFGSmethodgenerally,itmustadoptparticularsparsetechniqueforsolvinglargedimensionaloptimizationproblems.Toint(1981)proposedapartiallyseparableBFGSmethodforsolvingconvexpartiallyseparableminimization.Thereby,theHessianmatrixoftheobjectivefunctionbeingsimilartoablockdiagonalsparsematrixismaintainedbytheupdatedmatrixsequence.Toint(1982)obtainedlocalconvergenceofthepartiallyseparableBFGSmethodwhentheelementalobjectivefunctionsareconvex.Moreover,Toint(1986)obtainedglobalconvergenceofthismethodwithWolfe-Powelllinesearch.WeproposeamodificationoftheBFGSmethodbasedonthemodifiedBFGS(MBFGS)formulagivenbyLi-Fukushima(2001)forsolvingnonconvexpartiallyseparablemini-mization.It’soneofthemainachievementsofthispaper.Inthemethod,thesymmetricpositivesemidefinitematricesareupdatedtoapproximatetheHessianmatricesoftheelementalobjectivefunctionsandtheirsumtoapproximatetheHessianmatrixoftheobjectivefunction.Thereby,sparsityoftheHessianmatrixoftheobjectivefunctionismaintainedbytheapproximateupdatedmatrixsequence.Moreover,theupdatedmatrixsequenceisasymmetricpositivedefinitematrixsequence.Undersomeweakconditions,theglobalconvergencetheoremofthemethodisestablished.TheresultmayberegardedasanextensionofthepartitionedBFGSalgorithmproposedbyToint(1986).Theotherwestudyinthispaperislogisticsandsupplychainmanagement.ThenewandoldmodelofEDI,directEDIusingforspecialpurpose,EDIbasedonVAN,andEDIbasedonInternet(InternetMail,StandardIC,Wed-EDI,XML/EDI)arecomparedindetail,furtherstudiedandextensivelyexplored.Furthermore,thedomesticandinternationaldevelopmentsituationandperspectivesofEDIisanalyzedsystematically.ThestructuralchangesfromE-commercetoM-commerceanditsprofoundinfluenceareanalyzedsystematically.WefurtherstudyM-commerceasthenewopportunityof21centuryglobaldevelopment:theprimaryimpetusofneweconomy,thekeyreasonofacceleratingeconomyglobally,thekeycontentofpushingtradeglobally,andtheeffectivemeansofspeedingupfinancegloballyindetail.Thenweexploretechnology,serviceandenviron-mentalprotection,theseverechallengefacedbyM-commerceasacontesttocontendthe-III-IIIcommandingpointofeconomydevelopingcontinuouslyin21century.Finally,welookintothefutureofM-commerce.KeywordsNonconvexpartiallyseparableminimization;MBFGSmethod;Globalconvergence;EDI;InternetEDI;Value-addednetworks;M-commerce;WAP(WirelessApplicationProtocol)--IV1______2-1-111.11.1.1RRfn→:),(minxf.nxR∈1.11.1nRx∈0}{kx}{kx1.1}{kx1.1kx1+kxf1+kx)(1+kxf)(kxfkxkd,0)(∇kTkdxf)(xf∇fx,1kkkkdxxα+=+0kα)(kkkdxfα+)(kxfkαkα).(min0kkdxfαα+Armijo0kα,)()()(kTkkkkkkdxfxfdxf∇+≤+σαα)1,0(∈σkα},,,,1{32Λρρρ)1,0(∈ρWolfe-Powellkα-2-∇≥+∇∇+≤+,)()(,)()()(21kTkkTkkkkTkkkkkkdxfddxfdxfxfdxfσαασα1021σσ1.1.2NewtonNewtonNewtonNewtonNewtonHessianHessianHessianNewtonNewtonNewtonNewtonNewtonNewtonNewtonNewtonNewtonNewtonNewton1.1Newton0nRx∈0nnRB×∈00ε0:=k1ε≤∇||)(||kxfkx220)(=∇+kkxfdBkd33kα4kkkkdxxα+=+1ε≤∇||)(||1kxf1+kx5Newton1+kB1:+=kk2kkfB2∇=1.1NewtonNewtonNewtonkBNewtonkkkysB=+1kkkxxs−=+1kkkffy∇−∇=+1kkksfy12+∇≈NewtonkkfB2∇≈NewtonkBNewtonNewtonSR1kTkkkTkkkkkkkSRkyyHsyHsyHsHH)())(()1(1−−−+=+-3-3DFPkkTkkTkkkkTkTkkkDFPkyHyHyyHysssHH−+=+)(1BFGSkkTkkTkkkkTkTkkkBFGSksBsBssBsyyyBB−+=+)(1NewtonBFGSNewtonBFGSDFPNewtonWolfe-PowellBFGSNewtonWolfe-PowellPowell[1]BFGSWerner[2]BFGSfNewtonDai[3]WolfePowellBFGSMascarenhas[4]BFGSNewtonLi-Fukushima[5]BFGSMBFGSWolfePowellArmijoMBFGSBFGSMBFGS1.1.3MBFGSBFGSNewton[1,6,7,8,9]BFGS[10,11,12]MBFGSf:RRn→1()(),miifxfx==∑1.2if:),,1(miRRnnΚ=→x)(2xf∇iℵ1{0}.mii=∩ℵ=1.3()mifi,,1Λ=1=m1.2-4-m1ffHessian[13]1.2BFGSfHessianBFGS1nRx∈0mnmiiB1}{=:0k=2ks)1,0[∈kα||kz||=||kkkgsB+||kα≤||kg||,)(kkxgg=kgfkx∑==mikikBB13mi,,1Λ=BFGSkiB1+kiB4,1kkksxx+=+:1kk=+1ifxfHessian)(2kikixfB∇≈kB)(2kxf∇if[14]Wolfe-Powell[15]BFGS1.2fBFGS[3][5]BFGSMBFGS[10,13]1.2MBFGSf1.21.2.1WTO——ElectronicCommerceOECDEC-5-5BusinesstoBusinessBusinesstoConsumer[16]17211.2.2EDI2070EDIElectronicDataInterchangeEDIEDI[17]EDI20-6-70EDIMIS[18]EDIMISEDIEDIEDIEDIEDIVANEDIInternetEDIInternetMailStandardICWed-EDIXML/EDIEDIEDI1.2.310003G3G1250[19]++=[20]PC[21],-7-71981PC19911986PC1996[22]212121BFGSMBFGSMBFGSEDIEDI21-8-2BFGSMBFGS2.1BFGSBFGSMBFGS1.1NewtonBFGSBroyden[23]Fletcher[24],Goldfarb[25]Shanno[26]kB,1kkTkkTkkkkTkTkkkksBsBssBsyyyBB−=+2.1kkkxxs−=+1)()(1kkkxfxfy∇−∇=+2.1[27,28]2.1.11kBBFGSkB0kTksy1kB1kBkB0kTksy2.1kBkBfkdfkx2.1.1kB0kTksyf,0kTksyfWolfe-Powell0kTksyNewtonfkx1.1NewtonBFGS1+kB2.1BFGSBFGS[1,6,7,9,15,29,30]fWolfe-PowellBroydenBFGSByrdNocedal[7]ArmijoBFGSNewton[8,14,15,31,32,33,34,35,36,37,38],Wolfe-PowellBFGS[33,39]2.2BFGSMBFGSBFGSBFGS-