1、01 201min( ),. .( ), , , ( ),niif xxRs tc xiElc xiIlm 01 2min( ),. .( ), , , nif xxRs tc xiEl *()gf x c1(x)=01*()c x 110*()()f xc x -g*x*f(x)=f*12*(),()c xcx11220*()()()f xc xcx01 2min( ),. .( ), , , nif xxRs tc xiEl 1 2*()(, )ic xil12*,l10*()().liiif xc x 01 2min( ),. .( ), , , nif xxRs tc xiEl 1(

2、, )( )( )( )( )lTiiiL xf xc xf xc x 11( )( )( , )( ( ),( )lxiiiTlLf xc xL xLc xc x 11( )( )( , )( ( ),( )lxiiiTlLf xc xL xLc xc x 0*(,)L x 01 2min( ),. .( ), , , nif xxRs tc xiEl 0*(,)L x 01 2*(),(, , )Tisc xil20*(,)TxsL xs sx 0( ),jcx x 01 2min( ),. .( ), , ,nif xxRs tc xim 0( ),kcx x x 0( ) |( )iI

3、I xi c xx 01 2min( ),. .( ), , ,nif xxRs tc xim 010*()(),miiif xc x 01*(),iic xim 00 1*, ,iim 010*()(),miiif xc x 00 1*(), ,iic xim 00 1*, ,iim 00*()(),iii If xc x 00*, *.iiI d1*()c x 2*()cx 30( )cx 10( )c x 20( )cx *x0*(),Tidc xiI0*()Tf xd0*(),Tidc xiI0*()Tf xd0*|()nTSdRf xd0*|(),*nTiGdRc xdiI0*(),

4、Tf xd0*(),*Tic xdiI0*(),Tf xd0*(),*Tic xdiI*(),()()if xc xiI10.riiia 00*()(),iii If xc x 010*()(),miiif xc x 00 1*(), ,iic xim 00 1*, ,iim 010*()(),miiif xc x 01*(),iic xim 00 1*, ,iim 2121201232123 11022022013 1*(),()xxxxxx 311210*(),xx 210*,x 320*.x 00 1 2 3*, , , .ii 2121201232123 11022022013 1*(

5、),()xxxxxx 311210*(),xx 210*,x 320*.x 00 1 2 3*, , , .ii 01 2min( ),. .( ), , ,nif xxRs tc xim 10*()(),miiif xc x 01*(),iic xim 01*,iim *()ic x *x 0*()(*),Tic xdiI0*().Tf xd0*()(*)Tic xdiI0*().Tf xd0*()().iii If xc x 1riiiba a1a210*()(),miiif xc x 01*(),iic xim 01*,iim 01 2min( ),. .( ), , ,nif xxRs

6、 tc xim 10*()niiibxp 0*()Tiiiixp yc01 201min( ),. .( ), , , ( ),niif xxRs tc xiElc xiIlm *()ic x 10*()(),miiif xc x 0*(),iic xiI 0*,.iiI 10*()(),miiif xc x 1*( , )( )()miiiL xf xc x 0*(,).xL x 2221*(,)()()mxiiiL xf xc x *x 2*(,).xwL x 01 201min( ),. .( ), , , ( ),niif xxRs tc xiElc xiIlm *x 0*|(),nT

7、iMdRdc xiI0101min( ),. .( ), , ( ),nTiiiif xxRs tc xa xbiElc xiIlm 222123222112321231425332300000min( ). .( )( )( )( )( )f xxxxs tc xxxxcxxxcxxcxxcxx 624*()(,) ,Tf x 12 2 2*()( , , ) ,Tc x211 0*()(, , ) ,Tcx 12621022104200 1222*()()()f xc xcx 22200*(),cx0101min( ),. .( ), , ( ),niif xxRs tc xiElc xi

8、Ilm 2212121220min(,). .f x xxxs t xx 221212121222,(,),xxxxF x xxx 2221212122(,)()P x xxxxx12221( )( )xx 421 01 2min( ),. .( ), , , nif xxRs tc xiEl 11( ,)( )|( ) | ,liiP xf xc x 1( )|( ) | ,liiP xc x 00( ),( ),( ,)( ),ic xP xP xf x 00( ),( ),( ,)( )( ),ic xP xP xf xP x( ,)( )( ),P xf xP x( )P x01 2m

9、in( ),. .( ), , ,nif xxRs tc xiIm ( ,)( )( ),P xf xP x10010( )( )|( ) | ,( )imiiic xP xc xc x 10| min( ,( ) |miic x 12|( ) |( )()miiic xc x 2212110min( ). .f xxxs t x22212101( ,)min( ,)P xxxx22212101( ,)min( ,)P xxxx 22121222121110110,() ,xxxxxxx 111111212211,(),Pxxxxxx 222Pxx 120PPxx1201( ),( ).xx

10、221111( ,)()().P x 01 201min( ),. .( ), , , ( ),niif xxRs tc xiElc xiIlm ( ,)( )( ),P xf xP x11011( )|( ) | min( ,( ) |(,)lmijij lP xc xcx ( )P xmin( ,)( )( ),kkP xf xP x(),kkP x 11111(,)()()kkkkkP xf xP x11()()kkkf xP x 110,()kkkP x(,)kkP x 1(,)kkP x 11()()kkkf xP x ()()kkkf xP x 1()()kkkf xP x 111

11、()()kkkf xP x 11()() ()()kkkkkf xf xP xP x 111 ()()()()kkkkkP xP xf xf x 111 ()() ()()kkkkkkP xP xP xP x110() ()()kkkkP xP x1()()kkP xP x 1kk 1()()kkf xf x 12121min( ). .f xxxs t xx212121( ,)()P xxxxx12112xx 01 201min( ),. .( ), , , ( ),niif xxRs tc xiElc xiIlm ( ,)( )( ),kkP xf xP x0*(),P x *()()()

12、kf xf xP x ()()(,)kkkkkf xP xP x1()()kkf xf x 11(,)(,)kkkkP xP x ()(,)()kkkkkP xP xf x00pf0()kP xk ( )P x0( ).P x *()(,)()kkkf xP xf x 0().kkP x ()kkP x *()(,)()kkkf xP xf x 42112212220min( )()(). .f xxxxs txx()kkP x 01 2min( ),. .( ), , ,nif xxRs tc xiIm 01 2|( ), ,niDxRc xim( , )( )( )B x rf xrB x

13、11( )( )miiB xc x 1( )ln( )miiB xc x 11( )( )miiB xc x 1( )ln( )miiB xc x ( , )( )( )B x rf xrB x( )B x( )B xmin( ,)( )( ),kkB x rf xr B x(),kkr B x 31212113100min( )(). .f xxxs txx 3121212111131(, )()().B x x rxxrxx 21211101()()Brxxx 22210Brxx 1( )(,) ,Tx rrr()kkr B x01 2min( ),. .( ), , , nif xxRs

14、 tc xiEl 1( , )( )( )lijjL xf xcx 0*(,).xLL xL 22122230min( ). .f xxxxs tx 2212223( , )L xxxxx21( ,)( )( )liiP xf xc x 221223()xxx 212( ,)( )( )liiP xf xc x 10*(,)()()()lxiiiP xf xc xc x 0*().f x( , )( )L xP x 22122230min( ). .f xxxxs tx 22122232( , ,)()M xxxx 221223( , )()L xxxx222( )/P xx 22122230

15、min( ). .f xxxxs tx 22122232( , ,)()M xxxx 1102,Mxx 22122232min( , ,)()M xxxx 22023()().Mxx 0302( ,) .Tx 0min( ),. .( )nf xxRs tC x ( , )( )( )TL xf xC x*(,)()()()TL xf xC xf x*( )( )( ,)Tf xC xL x0min ( , *). .( )L xs tC x 0min ( , *). .( )L xs tC x 2( , ,)( , )( )( )TM xL xC xC x 0(,)()()()xkkkkkk

16、M xf xC xC x 0*()()f xC x 2min( ,)()( )( )( )TTkkkkM xf xC xC xC x 22121220min( ). .f xxxs t xx22212121212222(, ,)()()M x xxxxxxx 1121220()Mxxxx 2122220()Mxxxx 12222.xx 1122()kkxx 1211k 11211kk 1211* 12222xx 01 2min( ),. .( ), , ,nif xxRs tc xiIm 201 2min( ),. .( ), ,.niif xxRs tc xzim 222112( , , ,

17、)( )( ( )( ( ) .mmiiiiiiiM x zf xc xzc xz 222112( , , ,)( )( ( )( ( ) .mmiiiiiiiM x zf xc xzc xz 0( )iic x221( , , ,)( )iiiiM x zzc xu 2( )iiizc x 2101 2max( ,( ), ,iiizc xim 221102( , ,)( )max( ,( )miiiiM xf xc x 221102( , ,)( )max( ,( )miiiiM xf xc x 101 2()max ,()(), ,kikiikc xim 1 221/()max( (),

18、)mkiikic x 2212122min( ). .f xxxs txx22221212121022(, ,)max( ,()M x xxxxx 22212122222121212221222,(),xxxxxxxxxx 122xx 1120,Mxx 2220.Mxx 0 0( , ) .Tx 122.xx 0 0( , ) .Tx 22221212121222(),Mxxxxxx 122xx 1121220(),Mxxxx 2222 22(,) .Tx 122.xx 2122220(),Mxxxx 11202max( ,()kkxx 01max( ,)k 112011.k min( ),.

19、 .nTf xxRs tA xb aid22121212121212222462055000min( ). .f xxxx xxxxxxxs txx 1()f x1221424 426( )(,)Tf xxxxx14 6()( , )Tf x14 1 06 0 1()( , )( , )TTf x2110126min()f xp 2()f x26 2()( , )Tf x1221424 426( )(,)Tf xxxxx20 1( , )Tx 6166 2510155( , )( ,)( ,)TTT22201 462284/min()f xp ( )f x *( ),iii If xa 1(

20、).qAf x *( )iii If xa ( )qf xA ( )f x ( )f x ( ).qAf x ( )qf xA ( )qf xA ( )f x ( )f x ( )f x 00( ),().Tqqf xA uv A vv qA uv0( ),.Tqqf xA uv A v ( )qqqqqqqA Af xA A A uA A v 1()TTqqqqqqqA A A uA A AA v .qA u 0TqA v qqA AI ( )( )()( ).qqqqf xA Af xIA Af x ( ),()( ).qqqqqA uA Af x vIA Af x ()( ),qqpIA

21、 Af x ( )( )()( ).qqqqf xA Af xIA Af x ( )f x( )qqA Af x p( )f x2( )| .Tpf xp()( ),qqpIA Af x ( )( )( )TTTqpf xf xPf x qqqPIA A 222()qqqqqqqqqPIA AIA AA A A AqqIA A qqA AI 1()()TTTTTqqqqqqqPIA AIA A AA.qP ( )( )TTqqf xP Pf x 2|( ) |qPf x 0. 2|p 2TTqqqqqPPPP P ( )()( )qqqpPf xIA Af x 1()( )TTTTqqqqqq

22、A pAIA A AAf x 1()( )TTTTqqqqqqAA A A AAf x ( )f xp0. ( )()( )qqqpPf xIA Af x 0TqA p ()TTTqqqAxpA xA pTqqA xb()Tiiaxpb 0()TTiiia xba p 0,Tiia xb 0TiiTia xba p 0maxmin|TTiiiTia xba pa p ( ).qf xA ( ).qAf x ( )f x ( ).qf xA ( ).qAf x *( )qjjj If xAa *,iijjj Ij iaa ( )f x ( )f xia*,( )iijjj Ij if xaa (

23、 )f xia110( ),.Tqqf xAuv Av*,( )iijjj Ij if xaa 1111( )( )()( ).qqqqf xAAf xIAAf x 11( )qqiif xAa111,qqqPIAA 11( ).qqpPf x 1111( )( )()( ).qqqqf xAAf xIAAf x ( )f xia1qp 110( )qp 2112( )( )|Tqqpf xp 130*( )(,)TqjpajIji 10Tqipa 111,qqqPIAA 11( ).qqpPf x 11( )qqpPf x 11()iqqiiAAaa 110.qqiiAAaa 1111()(

24、)qqqqiiIAAAa 1qiAa 110qqiiAAaa 11( ),qqpPf x 11( )( )( )TTTqqpf xf xPf x 11( )( )TTqqf xPPf x 21|( ) |qPf x 0. 21|qp 21111,.TqqqqPPPP111,qqqPIAA 11( ),qqpPf x 111TTTiqiiqqiiiia pa AAaa a 111()qiqqiipAAaa 111,qqqPIAA 11111111()( )TTTTqqqqqqqApAIAAAAf x 1111111()( )TTTTqqqqqqAAAAAAf x 0. 0Tiiia a ( )q

25、Pf x PqI AqAq0( )qPf x( )qPf x0( )qPf x1( )qPf x Y給出初始可行點給出初始可行點x1,控制誤差控制誤差 0,令令k=1Ik=aixkbi,Ikf fPq, Ikf f PqI AqAqpk= -Pqgk.|pk| ?N =Aq+gk 0?STOP計算計算 max,一維搜索求一維搜索求 k,xk+1=xk+ kpk,k=k+1Y l=min i,給出給出Aq-1,PqI AqAqpk=-Pq-1gk.N計算流程計算流程投影梯度法投影梯度法22121212121212222462055000min( ). .f xxxx xxxxxxxs txx 1

26、221424 426( )(,)Tf xxxxx14 6()( , )Tf x11101501A 21001A 122222.PIA AIA AO210().Pf x21146()()(,) .TAf xf x 110A 11111()TTAA AA 110TA111PIA A 10110010 0001 111004016()pPf x 06 211723601 6maxmin(),/f xp2516 306maxmin , 112211122263025,.TTTTa pa pa xba xb 116, 21110 1( , ) .Txxp 11101501A 106p 25 0 0(,

27、, )Tb 100 x 11101501A 106p 25 0 0(, , )Tb 100 x 11011021501565 62305 16. 16max. 22622 3()(,) , , Tf xI 11101501A 20 1( , )Tx 21150A 2220,().PO Pf x12222()()Af xAf x 01 5611 52/ 2 528 5/ 11101501A 201x 21150A 2 528 5/ 115A 11111()TTAA AA 152626 111PIA A 151010152626 25 265 265 261 26/ 11125 265 2665

28、261 262/()/pPf x 70 1314 13/ 22262284 01 4maxmin(),/f xp11101501A 251p 25 0 0(, , )Tb 1 114 14maxmin , 12421214244111,.TTTTa pa pa xba xb 2731, 322235 31 24 31(/,/) .Txxp 201x 2232 31160 312()(/,/) , Tf xI 11101501A 25 0 0(, , )Tb 335 3124 31/x 115A 125 265 265 261 26/P 1325 265 2632 3105 261 26160 310/()/Pf x 1152626A 1332 311 265 2632 310160 31/()/Af x 120101min ( )() . .( ), , ( ),TTTiiiTiiif xx GxC xQP