优化设计共轭梯度matlab程序.doc

111%用阻尼牛顿法求课本93页第2题f(x1,x2)=(x1-2)4+(x1-2x2)2极小值(matlab语言)k=0;ptol=1.0e-5;xk=input(input x0:)itcl=1;1;while norm(itcl)=ptolf1=4*xk(1,1)3-24*xk(1,1)2+50*xk(1,1)-4*xk(2,1)-32;-4*xk(1,1)+8*xk(2,1);G=12*xk(1,1)2-48*xk(1,1)+50,-4;-4,8;dk=-inv(G)*f1;a=-(dk*f1)/(dk*G*dk);xk=xk+a*dk;itcl=a*dk;k=k+1;endf=(xk(1,1)-2)4+(xk(1,1)-2*xk(2,1)2;fprintf(n用阻尼牛顿法迭代 %d 次后得到 极小点x*及极小值f为:n,k); disp(xk); disp(f);input x0:1;1xk = 1 1用阻尼牛顿法迭代 27 次后得到 极小点x*及极小值f为: 2.0000 1.0000 1.3270e-0190%用共轭梯度法求课本93页第32题f(x1,x2)=1.5*xk(1)2+0.5xk(2)2-xk(1)*xk(2)-2*xk(1)的极小值(matlab语言)xk=input(input x0:)ptol=1.0e-5;k=2;while k=2 k=0; btk=0; dk=0; for k=0:2 gk=3*xk(1,1)-xk(2,1)-2;xk(2,1)-xk(1,1); dk=-gk+btk*dk; f1=gk; G=3,-1;-1,1; a=-(dk*f1)/(dk*G*dk); xk=xk+a*dk; gk1=3*xk(1,1)-xk(2,1)-2;xk(2,1)-xk(1,1); if norm(gk1)ptol break end btk=(norm(gk1)/norm(gk)2; end if norm(gk1)=ptol for i=1:2 f(1)=2*x0(1)2+2*x0(2)2-4*x0(1)-2*x0(1)*x0(2); f1=2*x0(1)-2*x0(2)-4;4*x0(2)-2*x0(1); f2=2,-2;-2,4; a=-(d(:,1)*f1)/(d(:,1)*f2*d(:,1); x2=x2+a*d(:,1); f(2)=2*x2(1)2+2*x2(2)2-4*x2(1)-2*x2(1)*x2(2); det1=f(1)-f(2); f1=2*x2(1)-2*x2(2)-4;4*x2(2)-2*x2(1); a=-(d(:,2)*f1)/(d(:,2)*f2*d(:,2); x2=x2+a*d(:,2); f(3)=2*x2(1)2+2*x2(2)2-4*x2(1)-2*x2(1)*x2(2); det2=f(2)-f(3); end f1=2*x2(1)-2*x2(2)-4;4*x2(2)-2*x2(1); if det1=det2 detm=det1; m=1; else detm=det2; m=2; end dk=x2-x0; x3=2*x2-x0; f(4)=2*x3(1)2+2*x3(2)2-4*x3(1)-2*x3(1)*x3(2); if (f(4)f(1)&(f(1)-2*f(3)+f(4)*(f(1)-f(3)-detm)20.5*detm*(f(1)-f(4)2) a=-(dk*f1)/(dk*f2*dk); x0=x3+a*dk; if m=1 d(:,m)=d(:,2); d(:,2)=dk; else d(:,2)=dk; end elseif f(3)f(4) x0=x2; else x0=x3; end k=k+1; endfx0=2*x0(1)2+2*x0(2)2-4*x0(1)-2*x0(1)*x0(2); fprin