中职 优化计算方法及其MATLAB程序实现第4章电子课件 高教版 .pdf

《中职 优化计算方法及其MATLAB程序实现第4章电子课件 高教版 .pdf》由会员分享，可在线阅读，更多相关《中职 优化计算方法及其MATLAB程序实现第4章电子课件 高教版 .pdf（35页珍藏版）》请在淘文阁 - 分享文档赚钱的网站上搜索。

1、1/35JJIIJIBackClosezO9MATLABSy1o?F2/35JJIIJIBackClose130?Fkg?5.?0?F0uFm?z,kQ-5,?(?,N?y.d?,Faq,?F?8I9F,;?(Hesse?)?O,l?$?O;,d,)?zK?k?.4.15?5?g:3)n?g8I4?:?)|?|,3(|eS“n=U?4?:.L?/?,5?2?)?g8I/.ek0?Vg.3/35JJIIJIBackClose4.1?A Rnn?,en|d1,d2,dm(m 6 n)vdTiAdj=0,i 6=j,Kd1,d2,dmA?.w,|?2,=?A=I(?),4.1C|?.d?,Jy?A?

2、|kXe5.K4.1?A Rnn?,e|d1,d2,dnA?,K5?.e)?g8I4?:?5?.?minxRnf(x)=12xTAx bTx,(4.1):An?;bn.Xe.4/35JJIIJIBackClose4.1(5?)0,S“0 6?1:x0 Rn.Og0=f(x0)=Ax0b.?d0?dT0g0 0.-k:=0.1,ekgkk 6,x xk.2,|(|(fk.3,-xk+1:=xk+kdk,Ogk+1=f(xk+1)=Axk+1 b.4,?dk+1ve5?5:dTk+1gk+1 f(xk+1)+gTk+1hk+1=f(xk+1)+kXi=0(i i)gTk+1di.eygTk+1di

3、=0,i=0,1,k(4.2)7/35JJIIJIBackClose=.,gj+1 gj=A(xj+1 xj)=jAdj,(4.3)?i dT0A,?0=dT0Ad1=dT0Ag1+0dT0Ad0.l)0|(4.3),?0=dT0Ag1dT0Ad0=gT1Ad0dT0Ad0=gT1(g1 g0)dT0(g1 g0)=gT1g1gT0g0.?B?d1?L./,31kgS“,-dk=gk+k1dk1+k2Xi=0(i)kdi,(4.6)10/35JJIIJIBackClosek1,(i)k(i=0,1,k 2)?LvdTkAdi=0,i=0,1,k 1.5?,d(4.1)di?(?,kgTkdi=

4、0,gTkgi=0,i=0,1,k 1.(4.7)(4.6)dTiA(i=0,1,k 1)|A?5,?0=dTk1Adk=dTk1Agk+k1dTk1Adk1(4.8)90=dTiAdk=dTiAgk+(i)kdTiAdi,i=0,1,k 2.(4.9)l(4.8)k1|(4.3)(4.7),?k1=dTk1AgkdTk1Adk1=gTkAdk1dTk1Adk111/35JJIIJIBackClose=gTk(gk gk1)dTk1(gk gk1)=gTkgkdTk1gk1=gTkgkgTk1gk1.(4.10)aq/,d(4.9)(i)k|(4.3)(4.7),?(i)k=dTiAgkdTi

5、Adi=gTkAdidTiAdi=gTk(gi+1 gi)dTi(gi+1 gi)=0,i=0,1,k 2.d,5?F?S“xk+1=xk+kdk,dk=gk+k1dk1,(4.11)d1=0,k1d(4.10)(.N?,u?g(4.4),(k=gTkdk/dTkAdk.n?,?)?g(4.4)4?:?Xe.12/35JJIIJIBackClose4.1(5?F)0,S“0 6?1:x0 Rn.Og0=Ax0 b,d0=g0.-k:=0.1,ekgkk 6,x xk.2,Ok=gTkdkdTkAdk,xk+1:=xk+kdk,gk+1=Axk+1 b,k=gTk+1AdkdTkAdk=gTk+

6、1gk+1gTkgk,dk+1=gk+1+kdk.3,-k:=k+1,=1.13/35JJIIJIBackClosen4.2?A Rnn?,K35Ke?g(4.4)4?:?5?Fm 6 nS“?,k0 6 k 6 m 1,kdTkgk=gTkgk,(4.12)dTkAdi=0,gTkgi=gTkdi=0,i 6 k 1,(4.13)spang0,g1,gk=spang0,Ag0,Akg0,(4.14)spand0,d1,dk=spang0,Ag0,Akg0.(4.15)y dn4.1,y?g5Iyd0,d1,dn1u?A?=,T(4.13)?1y?.ky(4.12).du?k 0,d(4.11

7、)9(|?5(4.7),kdTkgk=gTkgk+k1dTk1gk=gTkgk.14/35JJIIJIBackClosegy(4.13).?i 6 k 1,d5?di?4,?di=gi+i1di1=gi i1gi1+i1i2di2=gi i1gi1 i1i2gi2 i1Yj=0jg0.d,e?i 6 k 1,gTkgi=0,7kgTkdi=0.?IydTkAdi=0,gTkgi=0,i 6 k 1(4.16)=.8By(.?k=1,(dT1Ad0=0gT1g0=0.0?(|?5,(w,.?(4.16),k dTk|5K?59(4.12),?k=gTkdkdTkAdk=gTkgkdTkAdk6=

8、0.(4.18)d(4.11)(4.17),i 6 k,kgTk+1gi=gTkgi+kdTkAgi=gTkgi kdTkA(di i1di1).(4.19)u,?i=k,|8Bb?,d(4.18)(4.19),?gTk+1gk=gTkgk kdTkAdk=gTkgkgTkgkdTkAdkdTkAdk=0.?i k,d(4.19)8Bb?,kgTk+1gi=0.?,(4.16)?1?y.16/35JJIIJIBackClose,d(4.11)(4.17),i 6 k,kdTk+1Adi=gTk+1Adi+kdTkAdi=gTk+1(gi gi+1)/i+kdTkAdi.(4.20)?i=k,d

9、(4.10)!(4.18)(4.20),?dTk+1Adk=gTk+1(gk gk+1)/k+kdTkAdk=gTk+1gk+1dTkAdkgTkgk+gTk+1gk+1gTkgkdTkAdk=0.?i 1.y(4.14)k+1,Iygk+1 spang0,Ag0,Ak+1g0,gk+16 spang0,Ag0,Akg0=spand0,d1,dk,Zk.,d8Bb?,dkgkufmspang0,Ag0,Akg0.?Adkgkuspang0,Ag0,Ak+1g0.dgk+1=gk+kAdk?gk+1 spang0,Ag0,Ak+1g0.18/35JJIIJIBackClose2d?5,kgk+1

10、Zk.?egk+1 spang0,Ag0,Akg0=spand0,d1,dk,Kkgk+1=0,g,7kspang0,g1,gk+1=spang0,Ag0,Ak+1g0.l?(4.14)?y.y.?e4.1?MATLABSy.S4.1(5?FS)function k,x,val=linecg(A,b,x0,epsilon,N)%U:5?F)?K:%min f(x)=0.5*xT*A*x-bT*x%:An?,bn?,x0:,19/35JJIIJIBackClose%epsilonNN?,NS“g%:kS“g,x,valOCq:if nargin5,N=1000;endif nargin4,eps

11、ilon=1.e-5;endif nargin3,x0=zeros(length(b),1);endk=0;gk=A*x0-b;dk=-gk;while(kN)temp=A*dk;alpha=-gk*dk/(dk*temp);x=x0+alpha*dk;gk=A*x-b;20/35JJIIJIBackClosebetak=gk*temp/(dk*temp);dk=-gk+betak*dk;if(norm(gk)ex41k=1022/35JJIIJIBackCloseval=-101.0000=5?FSS“10gv?Cq4?f(x)101.4.35?F9MATLABy5?F3?g?4?:k?5,

12、Au?54?zKminxRnf(x)(4.21)?5?F.N/,5?F3zS“|?c:?e(KF)?c?5|?c?|,?d0=g0.23/35JJIIJIBackCloseHesteness!StiefelFletcher?Au?zK?L?J,5?Fd?c)?zK?-a.u5?F?|dk+1=gk+1+kdk,kkL/.e?A:k=gTk+1gk+1gTkgk(Fletcher-Reeves,FR),k=gTk+1gk+1dTkgk(Dixon),k=gTk+1gk+1dTk(gk+1 gk)(Dai-Yuan),(4.22)k=gTk+1(gk+1 gk)dTk(gk+1 gk)(Crowd

13、er-Wolfe),24/35JJIIJIBackClosek=gTk+1(gk+1 gk)dTk(gk+1 gk)(Hesteness-Stiefel,HS),k=gTk+1(gk+1 gk)gTkgk(Polak-Ribi ere-Polyak,PRP).e5?F)?zK(4.1)4?:?.4.2(5?F)0,S“0 6?1:x0 Rn.Og0=f(x0),d0=g0.-k:=0.1,ekgkk 6,x xk.2,|,|(|k,Oxk+1=xk+kdk,gk+1=f(xk+1).25/35JJIIJIBackClose3,#|dk+1:=gk+1+kdk,kd(4.22)?,(XFR)(.

14、4,-k:=k+1,=1.ey4.2?5n.n4.3?xkd4.2?)?S?,bf(x)?YY8L(x0)=x|f(x)6 f(x0)k.?,o4.2k,limkg(xk)=0.y”5,”b?xkS?.dkg(xk)6=0.dk=gk+k1dk1,?kgTkdk=kgkk2+k1gTkdk1=kgkk2 0,kf(x+d)=f(x)+g(x)Td+o()f(x),27/35JJIIJIBackClose=f(x+d)0,kf(xk+1)=f(xk+kdk)6 f(xk+dk).uk K2 K1,-k?4,?f(x)6 f(x+d)0,?kg(u)g(v)k 6 Lku vk,u,v Rn.e?

15、|dkgk?Y?kv0 6 k62,?0,2?.o4.2k,limkg(xk)=0.y”5,”b?xkS?.dLipschitz9YWolfeOK(2.12),?kLkdkk2 dTkg(xk+kdk)gk (1 )dTkgk=(1 )kdkkkgkkcosk,29/35JJIIJIBackClose=kkdkk(1 )Lkgkkcosk.u|9WolfeOK(2.11),?f(xk)f(xk+kdk)kdTkgk=kkdkkkgkkcosk(1 )Lkgkk2cos2k(1 )Lkgkk2sin2.5?f(x)ke.?,dJ?Xk=0kgkk2+,%?k ,kkgkk 0.y.?30/35J

16、JIIJIBackClose3?F?S,3S“nn+1?,-#?KF|,-m?F.u?g?,nS“?F?)?|2k?5.?u5?K,zm(m nm?n)?1-m.d?,?|e,?KF|.euArmijo(|?-mFR5?F?MATLABS.S4.2(FR5?FS)function k,x,val=frcg(fun,gfun,x0,epsilon,N)%U:FR5?F)?K:min f(x)%:fun,gfunO8I9F,x0:,%epsilonNN?,NS“g31/35JJIIJIBackCloseif nargin5,N=1000;endif nargin4,epsilon=1.e-5;en

17、dbeta=0.6;sigma=0.4;n=length(x0);k=0;while(k=0.0),dk=-gk;endendif(norm(gk)epsilon),break;end%u?m=0;mk=0;while(m20)%Armijo|if(feval(fun,x0+betam*dk).=feval(fun,x0)+sigma*betam*gk*dk)mk=m;break;endm=m+1;endx=x0+betamk*dk;g0=gk;d0=dk;33/35JJIIJIBackClosex0=x;k=k+1;endval=feval(fun,x);4.2|FR5?F(S4.2)?K)

18、?zKminxR2f(x)=2x21+x22 2x1x2 2x2.TKk()x=(1,2)T,f(x)=2.)k,?8I9F?mfun.mgfun.m:%8Ifunction f=fun(x)f=2*x(1)2+x(2)2-2*x(1)*x(2)-2*x(2);%F34/35JJIIJIBackClosefunction gf=gfun(x)gf=4*x(1)-2*x(2);2*x(2)-2*x(1)-2;,?,|S4.2,OK?kf(xk)k 6 105.?:,(JXL4.1?.L4.1 FR?F?(J:(x0)S“g(k)8I(f(xk)(0.0,0.0)T122.0000(1.0,1.0)T142.0000(5.0,5.0)T172.0000(10.0,10.0)T162.0000(8.0,8.0)T152.0000dL4.1w,FR?F?-x0=0.0;0.0;35/35JJIIJIBackClose k,x,val=frcg(fun,gfun,x0)fun,gfunO8I9F?m.