function x=lindual(c,A,b)
[n1,n2]=size(A)
A=[A,eye(n1)]c=[-c,zeros(1,n1)]
x1=[zeros(1,n2),b']lk=[n2+1:n1+n2]
while(1)
x=x1(1:n2)
s1=[lk',b,A]
c
x1
cc=[]ci=[]
for i=1:n1
if b(i)<0
cc=[cc,b(i)]
ci=[ci,i]
end
end
nc=length(cc)
if nc==0
fprintf('达到最优解')
break
end
cliu=cc(1)
cl=ci(1)
for j=1:nc
if abs(cc(j))>abs(cliu)
cliu=cc(j)
cl=j
end
end
cc1=[]ci1=[]
for i=1:n1+n2
if A(cl,i)<0
cc1=[cc1,A(cl,i)]
ci1=[ci1,i]
end
end
nc1=length(cc1)
if nc1==0
fprintf('无可行解')
break
end
cliu=c(ci1(1))/cc1(1)
cl1=ci1(1)
for j=1:nc1
if c(ci1(j))/cc1(j)<cliu
cliu=c(ci1(j))/cc1(j)
cl1=ci1(j)
end
end
b(cl)=b(cl)/A(cl,cl1)
A(cl,:)=A(cl,:)/A(cl,cl1)
for k=1:n1
if k~=cl
b(k)=b(k)-b(cl)*A(k,cl1)
A(k,:)=A(k,:)-A(cl,:).*A(k,cl1)
end
end
c=c-c(cl1).*A(cl,:)
x1(lk(cl))=0
lk(cl)=cl1
for kk=1:n1
x1(lk(kk))=b(kk)
end
x=x1(1:n2)
end
验证p62运筹学
min ω=2x1+3x2+4x3
x1+2x2+x3≥3
2x1-x2+3x3≥4
x1,x2,x3≥0
检验
format rat
c=[2 3 4]A=[-1 -2 -1-2 1 -3]b=[-3-4]
x=lindual(c,A,b)
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