线性规划的发展历史-(2)

(),1979,,,,,,25%50%,,,,,max{eTx}x:Ax=b,x}xcn,bm,,Amxn,xO1823Fourier1911poussin!!,,1939,Kantorovioh,,,,,,,,1960,,1941,Hitchck,1945,stigler,1947,Kpmans,,Dantzig1946,,,,,Leontief1932,,Dantzig,J7070,,,,,1,2x7o=140,70x704900,70!10,,IBM370168,150,,Dont:ig,,,1947,Dantzig,,Kpmans(),Koopmans,1947,Dantzig,,,,,Dantzig1948,KOopmansDantzig:?Dantzi:!,,Dant:19vonNeumann,vonNeumann294710,Dantzig,VonNeumann,,,vonNeumann,:Dantzi:,!,vonNoumann,Dantzig,FarkasNeumann,,,,,,,,30,Dantzig,AXbAin,AmDantg,,,(1981,,)t19531955,HoffmanBleDantzig1952,DantzigWolfeorden,,Charnes,1963,Wolfe,1976Blond,,1953,Dantzig,19,Beal,1956,Dant:19Fulkerson,1963Dontzig,,,,1951,FritzJQhnKuhnTucker,kafellerWolfecottle,1954,,FFUIKrnffman,1955,Dantzig955,DantZig,60,Wetscharne,1956,GOmory,,BalasLandDOig121963,Dant:Cottle,1965Lmk,70,scaKuhnEave1951,Cha;nesCp,,,,,,,,,,19581959,,,,,,,,,,,,261,,,;,,,,,nAB,AnZ,B2,K,,A,nZ=K,nAKB,2=K,nB=109:K100,,,100K,,AB,nA10K,nB=109:100+logZK7+109:K,,B,,6,,,,,,,,:?1972,KleeMinty,,,,,2,,,,,,!,?2.Khachiyan1979,Khachiyan(XaHH),ShorJudinNemirovski,,o(nL),n,L,,,Khachiyan1982Fulkerson27,max{CTxx:Axb,xO}(AP),,Axb(AP),,(AP),(AP),,,,,,,,,(AP),,,,,,,,,,,,1982,BerkeleySmal,(m,n)C(m,P)nC(m,P),pp=1,n1952,Borgwart,max{vx!X:AXi},0(n4m)3Karmarkar,19849,Bell32Karmarkar,0(n6L),5000,50Karmarkar,,Karmarkar1955,FrischminCTglogxj,Ax=,,,,,Huard,;Elogx,,Karmarkarmin{eTxlx:Axb,xO}Karmarkarminn{eTx}x:Ax=o,xi=eTxx,x}(==o)n{x!Ax,(,,xn,,=,*b,x}(=o),,x,,X),(al,,a),x;=(z,~,X.)~ai,xn1,(a,,,)e,Ax=bl+lAx0,CTxcTx,{xk},f(x)=:109Xjf(x)f(x)6,,n1x(Y)cTx(Y1),,Karmarkar,,,KarmarkarDantzig,,,,,,,,,,,,,,1G.BDantzig,,,Vol3,Nol,19842:,,vo12,N01,19833:,NoZ,19854:(1939),,19595:,,19836K.GMurty,Linearprogramming,JohnWiley&sons,NewYorks19837C.BDantzig,UniversityPress,LinearProgrammingandExtensions,PrineetonO,8A.Charnes,W.WPrineeton,NJ1963CoPPer,andAHenderson,AnIntroduetionLinarprogramg,wiley,NewYork,19539LRFOrd,Jr,andDR,Fulkerson,FlowsinNetworks,PrineetonUniversityPress,PrineetonNJ.,196210MBazaraaandJJJarvis,LinearProgrammingandNetworkFlows,WileysNewYork,197711CH.Papadimitriou,Combinatorialoptimi:ation:AlgorithmsandComploxity,PrentieeHall,Ine,EnglewoodCliffs,NJ,198212NKarmarkar,ANewpolynomialtimeAlgorithmforLinearprogram-ming,inproeeedingsof16thannualACMsymPosiumontheoryofeomPutingWashingtonDC,198430