中职 优化计算方法及其MATLAB程序实现第6章电子课件 高教版 .pdf

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1、1/31JJIIJIBackClosezO9MATLABSy18&62/31JJIIJIBackClose?)?zKminxRnf(x)(6.1)?&6.|?,&6z?y?-.?U3zzgS“?,l?(#?S“:.?:|k?)(|),?(?(|);?&6K?(,?)#?S“:.&6?g:k?/&60?.,?cS“:%,d/.0/x/O0(?/&60?4.,?,L)S?/&6fK0(8I?gCq?.)?:5(/0.e U8Ik?e,K?T#?,?*&6,UY#?3/31JJIIJIBackCloseS“;K,?g?.8I?Cq?n,I?&6,2L)#?&6S?fK?#?.Xd-Ee?,?vS“.

2、6.1&6?(?kw&6?.?.?xk1kgS“:.Pfk=f(xk),gk=f(xk),BkHesse?2f(xk)?1kgCq.&6?.?8I?qk(d)=fk+gTkd+12dTBkd,Kw,kqk(0)=fk.u,1kgS“?&6fKkXe/:min?qk(d)|d Rn,kdk 6 k?,(6.2)4/31JJIIJIBackClose:k&6;k k?,?2-.?fK(6.2)?)dk,fkf31k?Se:fk=fk f(xk+dk),qkA?e:qk=qk(0)qk(dk).2?rk=fkqk.(6.3)/,kqk 0.d,erk 0,Kfk 0,xk+dkUeS“:,I?&6-

3、#)fK.erk?C1,?g?.8I3&6Sk?Cq,d5/31JJIIJIBackClosexk+1:=xk+dk#?S“:,egS“O&6.u,&6?C.e)?zK&6?e.6.1(&6)0,?0 6 1 2 1,0 1 1 0&6?,&60(0,.-k:=0.1,Ogk=f(xk).ekgkk 6,xCq4?:.2,)fK(6.2)?)dk.3,U(6.3)Ork?.6/31JJIIJIBackClose4,?&6.k+1:=1k,rk6 1,k,1 rk 2,kdkk=k.(6.4)5,erk 1,K-xk+1:=xk+dk,#?Bk?Bk+1,-k:=k+1,=1;K,xk+1:=x

4、k,-k:=k+1,=2.5 36.1,|?1=0.05,2=0.75,1=0.5,2=2.0,0=10=110kg(x0)k.3SO,?1N?,?ZO?J.dufK(6.2)?1k.48,d,6.12?dk3,=fK(6.2)?.e?nxkK(6.1)?-:,K?eqk 0.d,6.1?.7/31JJIIJIBackClosen6.1?dkfK(6.2)?).egk=f(xk)6=0,Kqk=qk(0)qk(dk)0.y 0fK(6.2)?1:,d,qk(dk)6 qk(0),=qk 0.eIyqk6=0.Xe,qk=qk(0)qk(dk)=0,Kqk(dk)=qk(0).?0fK(6.2)

5、?).?01?S:,?kqk(0)=0,=f(xk)=0,n?b?g.y.?|n6.1yd6.1?)?S?f(xk)NO?.ukXe.6.1?xkd6.1?)?S“S?,KS?f(xk)NO?.y d(?,?k 0,erk6 1,Kxk+1:=xk,8/31JJIIJIBackClosedkf(xk+1)=f(xk).erk 1,dn6.19rk?f(xk)f(xk+1)=f(xk)f(xk+dk)=rkqk 0,=f(xk+1)0.(6.6)9/31JJIIJIBackCloseNykdckk=kk6 k,=:1:,1uf(x)3xk?KF(e).e?n:dck5?g?.?e.n6.1d(6

6、.5)?:dckvqk(0)qk(dck)12kgkkmin?k,kgkkkBkk?.(6.7)y(1)egTkBkgk6 0,Kd(6.5)(6.6),kdck=kkgkkgk.dkqk(0)qk(dck)=fk qk?kkgkkgk?=gTk?kkgkkgk?12?kkgkkgk?TBk?kkgkkgk?10/31JJIIJIBackClose=kkgkkkgkk2122kkgkk2gTkBkgkkkgkkkgkk2=kkgkk(5?gTkBkgk 0)12kgkkmin?k,kgkkkBkk?.(2)egTkBkgk 0kgkk3kgTkBkgk6 1,Kdck=kgkk2gTkBkgk

7、gk,l?kqk(0)qk(dck)=fk qk?kgkk2gTkBkgkgk?=gTk?kgkk2gTkBkgkgk?12?kgkk2gTkBkgkgk?TBk?kgkk2gTkBkgkgk?11/31JJIIJIBackClose=12kgkk4gTkBkgk12kgkk2kBkk12kgkkmin?k,kgkkkBkk?.egTkBkgk 0kgkk3kgTkBkgk 1,Kdck=kkgkkgk9kgkk3kgTkBkgk,kqk(0)qk(dck)=fk qk?kkgkkgk?=gTk?kkgkkgk?12?kkgkkgk?TBk?kkgkkgk?=kkgkkkgkk2122kkgk

8、k2gTkBkgk12kkgkk 12kgkkmin?k,kgkkkBkk?.L3e,(6.7).y.?12/31JJIIJIBackClose6.2?dk&6fK(6.2)?),Kkqk(0)qk(dk)12kgkkmin?k,kgkkkBkk?.(6.8)y duqk(dk)6 qk(dck),dn6.1=?(.y.?e6.1?5n.n6.2b?36.1?=0,f(x)ke.,?x0 Rn,f3Y8L(x0)=x Rn|f(x)6 f(x0)Y.q?dkfK(6.2)?),?S?Bkk.,=3M 0,?kvkBkk 6 M.oegk6=0,K7kliminfkkgkk=0.13/31JJI

9、IJIBackClosey”5,?gk6=0,Kdrk?,k|rk 1|=?fk f(xk+dk)qk(0)qk(dk)qk(0)qk(dk)?=?f(xk+dk)qk(dk)qk(0)qk(dk)?.(6.9)5?d?V,kf(xk+dk)=fk+gTkdk+Z10dTkg(xk+tdk)gkdt.d,?k 0?,?|f(xk+dk)qk(dk)|=?12dTkBkdkZ10dTkg(xk+tdk)gkdt?612Mkdkk2+o(kdkk).(6.10)eyyn?(.?30 0?kgkk 0.u14/31JJIIJIBackClosed(6.8)(6.10),?|rk 1|612Mkdkk

10、2+o(kdkk)12kgkkminnk,kgkkkBkko6M2k+o(k)0minnk,0Mo=O(k).L,3?0,?vk6?k,k|rk 1|6 1 2,=rk 2.6.1kk+1 k.?3?k0 0,?vk6?k k0,kk.(6.11),?,b3kvrk 1,Kdrk?(6.8),?k k0,kfk fk+1 1qk(0)qk(dk)120minnk,0Mo.15/31JJIIJIBackClosef(x)ke.,Xk 0(k ),(6.11)g.2bu?k,krk 1.dk1(0,l?n?(.y.?6.3&6fK?)&6fK?)y?.&6fK(6.2)8I?g?zK.?)TfK?

11、,X!?F9A?)?24.?0?)&6fK?#.ke?n.16/31JJIIJIBackClosen6.3dfKmin qk(d)=fk+gTkd+12dTBkd,s.t.kdk26 k(6.12)?),?=?(Bk+I)d+gk=0,0,2k kdk22 0,(2k kdk22)=0,(6.13)?Bk+I?.:R+R2 R(,a,b):=a+b p(a b)2+42.(6.14)JTkXe5:(0,a,b)=0 a 0,b 0,ab=0.17/31JJIIJIBackClose-z=(,d)R+R+Rn.u,K(6.13)?duH(z):=H(,d)=?,2k kdk22?(Bk+I)d+

12、gk=0,(6.15)(,2kkdk22)=kdk22+2kq(+kdk22 2k)2+42.(6.16)Jy,?0,d(6.16)?Y?,k0(,2k kdk22)=4p(+kdk22 2k)2+42,0(,2k kdk22)=1 +kdk22 2kp(+kdk22 2k)2+42:=1 k,0d(,2k kdk22)=2dT?1+kdk22 2kp(+kdk22 2k)2+42?18/31JJIIJIBackClose:=2(1+k)dT.?0,H()Y?,Jacobi?H0(z)=100002(1+k)dT0dBk+I.(6.17)Jy,eBk?,K?z=(,d)R+R+Rn,Jacob

13、i?H0(z)?.(0,1),K(z)=kH(z)kmin1,kH(z)k.(6.18)6.2()fK?1w)0,?,(0,1),0 0,0 0,d0 Rn,-z0:=(0,0,d0),z:=(0,0,0).?(0,1)19/31JJIIJIBackClose0 19kH(z0)k 1.-i:=0.1,XJkH(zi)k=0,;K,Oi=(zi).2,)e?|H(zi)+H0(zi)zi=i z,(6.19)?)zi=(i,i,di).3,?mive?K?:kH(zi+mzi)k 6 1 (1 0)mkH(zi)k.(6.20)-i:=mi,zi+1:=zi+izi.4,-i:=i+1,=1.

14、6.2?595n?yaquz1,d?y.e6.2?MATLABS.20/31JJIIJIBackCloseS6.1|1w)&6fK,u(Cq)Hesse?/.function d,val,lam,i=trustq(fk,gk,Bk,deltak)%U:)&6fK:%min qk(d)=fk+gk*d+0.5*d*Bk*d,s.t.|d|=delta%:fkxk?8I,gkxk?F,%Bk1kgCqHesse?,delta?c&6%:d,valOfK?:,lamf,iS“g,n=length(gk);beta=0.6;sigma=0.2;mu0=0.05;lam0=0.05;gamma=0.05

15、;d0=ones(n,1);z0=mu0,lam0,d0;zbar=mu0,zeros(1,n+1);21/31JJIIJIBackClosei=0;%iS“gz=z0;mu=mu0;lam=lam0;d=d0;while(i=150)H=dah(mu,lam,d,gk,Bk,deltak);if(norm(H)=1.e-8)break;endJ=JacobiH(mu,lam,d,Bk,deltak);b=psi(mu,lam,d,gk,Bk,deltak,gamma)*zbar-H;dz=Jb;dmu=dz(1);dlam=dz(2);dd=dz(3:n+2);m=0;mi=0;while(

16、m20)22/31JJIIJIBackCloset1=betam;Hnew=dah(mu+t1*dmu,lam+t1*dlam,d+t1*dd,gk,Bk,deltak);if(norm(Hnew)fk=-5;gk=400-200;Bk=1202-400;-400 200;deltak=5;d,val,lam,i=trustq(fk,gk,Bk,deltak)26/31JJIIJIBackClose?d=-0.00001.0000val=-105lam=5.9880e-016i=5=S“5g?fK?)d=(0,1)Tqk(d)=105.27/31JJIIJIBackClose6.4&6?MAT

17、LABy?!.&6?MATLABS,3,TS?.&6,&6fK?Bk?8I?Hesse?Gk=2f(xk).S6.2(.&6?MATLABS)function k,x,val=trustm(x0,epsilon)%U:.&6)?zK:min f(x)%:x0S“:,epsilonNN?%:kS“g,x,valOCq4?:Cq4?n=length(x0);eta1=0.1;eta2=0.75;tau1=0.5;tau2=2.0;delta=1;dtabar=2.0;x=x0;Bk=Hess(x);k=0;28/31JJIIJIBackClosewhile(k50)fk=fun(x);gk=gfu

18、n(x);if(norm(gk)epsilon)break;end%NfStrustqd,val,lam,i=trustq(fk,gk,Bk,delta);deltaq=fk-val;deltaf=fun(x)-fun(x+d);rk=deltaf/deltaq;if(rk=eta2&norm(d)=delta)delta=min(tau2*delta,dtabar);elsedelta=delta;endendif(rketa1)x=x+d;Bk=Hess(x);endk=k+1;endval=fun(x);30/31JJIIJIBackClose6.2|.&6(S6.2)?zKminxR2

19、f(x)=100(x21 x2)2+(x1 1)2.(6.21)TKk()x=(1,1)T,f(x)=0.)k,?8I9FHesse?nmfun.m!gfun.mHess.m:%8Ifunction f=fun(x)f=100*(x(1)2-x(2)2+(x(1)-1)2;%Ffunction gf=gfun(x)gf=400*x(1)*(x(1)2-x(2)+2*(x(1)-1);-200*(x(1)2-x(2);%Hesse?31/31JJIIJIBackClosefunction He=Hess(x)He=1200*x(1)2-400*x(2)+2,-400*x(1);-400*x(1),200;,?,|S6.2,OK?kf(xk)k 6 106.?:,(JXL6.1?.L6.1&6?(J:(x0)S“g(k)8I(f(xk)(0.0,0.0)T143.4655 1017(1.0,1.0)T101.6610 1016(1.0,1.0)T242.1162 1019(1.0,1.0)T204.8411 1015(8.0,5.0)T251.9289 1013(11.0,11.0)T185.7428 1023 u8I?zK?),INL?U8I!FHesse?nfS(fun,gfun,Hess)=.