matlab.zip_matlab 复合形法_matlab复合形法_复合形_复合形法

%用复合形法求函数f=4*x1-x2^2-12的最优解 %约束条件是g1=x1^2+x2^2-25<=0,g2=-x1<=0,g3=-x2<=0 %已知初始顶点是x01=[2 1],x02=[4 1],x03=[3 3] syms x1 x2 x01 x02 x03 disp('请输入第一点x01'); x01=input('x01>>'); disp('请输入第二点x02'); x02=input('x02>>'); disp('请输入第三点x03'); x03=input('x03>>'); disp('请输入收敛精度ee'); e=input('e>>'); k=0;ee=1.0;a=1.3;r=1.0;b=0.7;t=1; sign0=1;sign1=1;sign2=1;sign3=1;sign4=1; f=4*x1-x2^2-12; g1=x1^2+x2^2-25;g2=-x1;g3=-x2; f1=double(subs(f,{x1,x2},{x01(1),x01(2)})); f2=double(subs(f,{x1,x2},{x02(1),x02(2)})); f3=double(subs(f,{x1,x2},{x03(1),x03(2)})); ff=[g1;g2;g3];xx=[x01;x02;x03]; while ee>e k=k+1 for i=1:3 for j=1:3 gg=double(subs(ff(i),{x1,x2},{xx(j,1),xx(j,2)})); if gg>0 sign0=0; end end end if sign0==0 disp('顶点不在可行域内,请重新输入') break; end if f1>f2&f1>f3&f2>f3 xh=x01;xl=x03;fh=f1;fl=f3;t=1; elseif f1>f2&f1>f3&f2<f3 xh=x01;xl=x02;fh=f1;fl=f2;t=1; elseif f1>f2&f1<f3 xh=x03;xl=x02;fh=f3;fl=f2;t=3; elseif f1<f2&f1>f3 xh=x02;xl=x03;fh=f2;fl=f3;t=2; elseif f1<f2&f1<f3&f2>f3 xh=x02;xl=x01;fh=f2;fl=f1;t=2; elseif f1<f2&f1<f3&f2<f3 xh=x03;xl=x01;fh=f3;fl=f1;t=3; end xc=0.5*(x01+x02+x03-xh) for i=1:3 gg=double(subs(ff(i),{x1,x2},{xc(1),xc(2)})); if gg>0 sign1=0;break; else sign1=1; end end if sign1==0 disp('点xc不在可行域内,请重新输入'); break; end for i=1:3 xr=xc+a*(xc-xh); for i=1:3 gg=double(subs(ff(i),{x1,x2},{xr(1),xr(2)})); if gg>0 sign2=0;break; else sign2=1; end end if sign2==1 xh=xr;break; end a=0.7*a; end if sign2==1&double(subs(f,{x1,x2},{xr(1),xr(2)}))<double(subs(f,{x1,x2},{xc(1),xc(2)})) xe=xr+r*(xr-xc); for i=1:3 gg=double(subs(ff(i),{x1,x2},{xe(1),xe(2)})); if gg>0 sign3=0;break; else sign3=1; end end if sign3==1&double(subs(f,{x1,x2},{xe(1),xe(2)}))<double(subs(f,{x1,x2},{xr(1),xr(2)})) xh=xe; end end if sign2==0 xk=xh+b*(xc-xh); for i=1:3 gg=double(subs(ff(i),{x1,x2},{xk(1),xk(2)})); if gg>0 sign4=0;break; else sign4=1; end end if sign4==1&double(subs(f,{x1,x2},{xk(1),xk(2)}))<double(subs(f,{x1,x2},{xh(1),xh(2)})) xh=xk; else x01=xl-0.5*(xl-x01);x02=xl-0.5*(xl-x02);x03=xl-0.5*(xl-x03); end end if t==1 x01=xh; elseif t==2 x02=xh; else x03=xh; end f1=double(subs(f,{x1,x2},{x01(1),x01(2)})); f2=double(subs(f,{x1,x2},{x02(1),x02(2)})); f3=double(subs(f,{x1,x2},{x03(1),x03(2)})); ee=sqrt(1/3*((f1-fl)^2+(f2-fl)^2+(f3-fl)^2)); end xl subs(f,{x1,x2},{xl(1),xl(2)})