机械优化设计MATLAB程序

机械优化设计作业1.用二次插值法求函数221ttt极小值，精度e=0.01。在MATLAB的M文件编辑器中编写的M文件，如下：f=inline('(t+1)*(t-2)^2','t')a=0;b=3;epsilon=0.01;t1=a;f1=f(t1);t3=b;f3=f(t3);t2=0.5*(t1+t3);f2=f(t2);c1=(f3-f1)/(t3-t1);c2=((f2-f1)/(t2-t1)-c1)/(t2-t3);t4=0.5*(t1+t3-c1/c2);f4=f(t4);k=0;while(abs(t4-t2)=epsilon)ift2t4iff2f4f1=f2;t1=t2;t2=t4;f2=f4;elsef3=f4;t3=t4;endelseiff2f4f3=f2;t3=t2;t2=t4;f2=f4;elsef1=f4;t2=t4;endendc1=(f3-f1)/(t3-t1);c2=((f2-f1)/(t2-t1)-c1)/(t2-t3);t4=0.5*(t1+t3-c1/c2);f4=f(t4);k=k+1;end%输出最优解iff2f4t=t4;f=f(t4);elset=t2;f=f(t2);endfprintf(1,'迭代计算k=%3.0f\n',k)fprintf(1,'极小点坐标t=%3.0f\n',t)fprintf(1,'函数值f=%3.4f\n',f)运行结果如下：迭代计算k=7极小点坐标t=2函数值f=0.00012.用黄金分割法求函数32321ttt的极小值，精度e=0.01。在MATLAB的M文件编辑器中编写的M文件，如下：f=inline('t^(2/3)-(t^2+1)^(1/3)','t');a=0;b=3;epsilon=0.01;t1=b-0.618*(b-a);f1=f(t1);t2=a+0.618*(b-a);f2=f(t2);k=1;whileabs(b-a)=epsiloniff1f2b=t2;t2=t1;f2=f1;t1=b-0.618*(b-a);f1=f(t1);elsea=t1;t1=t2;f1=f2;t2=a+0.618*(b-a);f2=f(t2);endt=0.5*(b+a);k=k+1;f0=f(t);endfprintf(1,'迭代次数k=%3.0f\n',k)fprintf(1,'迭代区间—左端a=%3.4f\n',a)fprintf(1,'试点1坐标值t1=%3.4f\n',t1)fprintf(1,'函数值f1=%3.4f\n',f(t1))fprintf(1,'迭代区间—右端b=%3.4f\n',b)fprintf(1,'试点2坐标值t2=%3.4f\n',t2)fprintf(1,'函数值f2=%3.4f\n',f(t2))fprintf(1,'区间中点t=%3.4f\n',t)fprintf(1,'函数值f0=%3.4f\n',f(t))运行结果如下：迭代次数k=13迭代区间—左端a=0.0000试点1坐标值t1=0.0036函数值f1=-0.9767迭代区间—右端b=0.0093试点2坐标值t2=0.0058函数值f2=-0.9679区间中点t=0.0047函数值f0=-0.9721由黄金分割法在初始区间[0，3]求得的极小值点为t=0.0047，极小值为-0.9721。3.用牛顿法、阻尼牛顿法及变尺度法求函数221412122,xxxxxf的极小点。(1)在用牛顿法在MATLAB的M文件编辑器中编写的M文件，如下：function[x,fx,k]=niudunfa(x0)symsx1x2f=(x1-2)^4+(x1-2*x2)^2;fx=0;v=[x1,x2];df=jacobian(f,v);df=df.';G=jacobian(df,v);epson=1e-12;g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});G1=subs(G,{x1,x2},{x0(1,1),x0(2,1)});k=0;p=-G1\g1;x0=x0+p;while(norm(g1)epson)p=-G1\g1;x0=x0+p;g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});G1=subs(G,{x1,x2},{x0(1,1),x0(2,1)});k=k+1;endx=x0;fx=subs(f,{x1,x2},{x(1,1),x(2,1)});运行结果如下：[x,fx,k]=niudunfa([1;1])x=1.99995544760595233814899913778970.99997772380297616907449956889483fx=0.0000000000000000039398907941382470301534502947647k=23(2)用阻尼牛顿法在MATLAB的M文件编辑器中编写的M文件，如下：function[x,fx,k]=zuniniudunfa(x0)%阻尼牛顿法symsx1x2f=(x1-2)^4+(x1-2*x2)^2;fx=0;v=[x1,x2];df=jacobian(f,v);df=df.';G=jacobian(df,v);epson=1e-12;%停机原则g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});G1=subs(G,{x1,x2},{x0(1,1),x0(2,1)});k=0;%迭代次数p=-G1\g1;a0=-p'*g1/(p'*G1*p);x0=x0+a0*p;while(norm(a0*p)epson)p=-G1\g1;a0=-p'*g1/(p'*G1*p);x0=x0+a0*p;g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});G1=subs(G,{x1,x2},{x0(1,1),x0(2,1)});k=k+1;endx=x0;fx=subs(f,{x1,x2},{x0(1,1),x0(2,1)});运行结果如下：[x,fx,k]=zuniniudunfa([1;1])x=1.99995544760595233814899913778970.99997772380297616907449956889483fx=0.0000000000000000039398907941382470301534502947647k=23(3)用变尺度法在MATLAB的M文件编辑器中编写的M文件，如下：4.用共轭梯度法求函数12122212122123,xxxxxxxf的极小点（1）用共轭梯度法在MATLAB的M文件编辑器中编写的M文件，如下：function[y,x,k]=CG(A,b,c,x0)%共轭梯度法解minf（x）=0.5*X'*A*X+b'x+ceps=1e-6;%迭代停机原则%fx=0.5*x0'.*A.*x0+b'.*x0+c;r0=A*x0+b;ifnorm(r0)=epsx=x0;y=0.5*x'*A*x+b'*x+c;k=0;endp0=-r0;a=-r0'*p0/(p0'*A*p0);x1=x0+a*p0;r1=A*x1+b;k=0;whilenorm(r1)epsbeta=(r1'*r1)/(r0'*r0);p1=-r1+beta*p0;alpha=-(r1'*p1)/(p1'*A*p1);x1=x1+alpha*p1;r2=A*x1+b;p0=p1;r0=r1;r1=r2;k=k+1;endx=x1;y=0.5*x'*A*x+b'*x+c;运行结果如下：[y,x,k]=CG([3-1;-11],[-2;0],0,[2;1])y=-1x=1.00001.0000k=1(2)用变尺度法在MATLAB的M文件编辑器中编写的M文件，如下：function[x,fx,k]=bianchidufa(A,b,c,x0)%用变尺度法求fx=0.5*x'*A*x+b'*x+c;epson=1e-12;g0=A*x0+b;G0=A;H0=eye(2);k=0;d0=-H0*g0;a0=-d0'*g0/(d0'*G0*d0);s0=a0*d0;%x(k+1)-x(k);y0=A*a0*d0;%g(k+1)-g(k);x1=x0+a0*d0;while(norm(s0)=epson)switchkcase{10}x0=x1;g0=A*x0+b;H0=eye(2);k=0;d0=-H0*g0;a0=-d0'*g0/(d0'*G0*d0);s0=a0*d0;x1=x0+a0*d0;breakotherwiseg1=A*x1+b;y0=A*a0*d0;s0=a0*d0;%H1=H0+s0*s0'/(s0'*y0)-H0*y0*y0'*H0/(y0'*H0*y0);H1=H0+((1+y0'*H0*y0/(s0'*y0))*s0*s0'-H0*y0*s0'-s0*y0'*H0)/(s0'*y0);k=k+1;d1=-H1*g1;a1=-d1'*g1/(d1'*G0*d1);a0=a1;d0=d1;H0=H1;s0=a0*d0;x1=x1+a0*d0;breakendendx=x1;fx=0.5*x1'*A*x1+b'*x1+c;运行结果如下：》[x,fx,k]=bianchidufa([3-1;-11],[-2;0],0,[2;1])H1=0.40310.25780.25780.8945fx=-1x=1.00001.0000fx=-1k=1故函数极小点是点（1,1）5.用鲍威尔法求函数211222121242,xxxxxxxf的极小点。用鲍威尔法在MATLAB的M文件编辑器中编写的M文件，如下：function[x,fx,k]=bowell(A,b,c,x0)%鲍威尔法d01=[1;0];d02=[0;1];x02=[0;0];esp=1e-12;%停机原则k=0;%迭代次数whilenorm(x0-x02)=espk=k+1;g01=A*x0+b;a01=-d01'*g01/(d01'*A*d01);x01=x0+a01*d01;g02=A*x01+b;a02=-d02'*g02/(d02'*A*d02);x02=x01+a02*d02;d10=x02-x0;g10=A*x02+b;a10=-d10'*g10/(d10'*A*d10);x10=x0+a01*d01;d01=d02;d02=d10;x0=x10;endx=x0;fx=0.5*x'*A*x+b'*x+c;运行结果如下：[x,fx,k]=bowell([2-2;-24],[-4;0],0,[2;1])fx=-8x=42fx=-8k=36.用单纯形法求线性规划问题)4,3,2,1(0535.224..4.43.32.21.1)(min43213214321jxxxxxxxxtsxxxxxfj用单纯形法在MATLAB的M文件编辑器中编写的M文件，如下：%单纯形法matlab程序-danchunxingfa%求解标准型线性规划:maxc*x;s.t.A*x=b;x=0%本函数中的A是单纯初始表，包括:最后一行是初始的检验数，最后一列是资源向量b%N是初始的基变量的下标%输出变量sol是最优解,其中松弛变量（或剩余变量）可能不为0%输出变量val是最优目标值，kk是迭代次数function[sol,val,kk]=danchunxingfa(A,N)[mA,nA]=size(A);kk=0;%迭代次数flag=1;whileflagkk=kk+1;ifA(mA,:)=0%已找到最优解flag=0;sol=zeros(1,nA-1);fori=1:mA-1sol(N(i))=A(i,nA);endval=-A(mA,nA);elsefori=1:nA-1ifA(mA,i)0&A(1:mA-