I try to solve the following simple LP Problem.
cvx_begin
variable L1 nonnegative;
variable L2 nonnegative;
variable L3 nonnegative;
variable L4 nonnegative;
dual variable D{3};
maximize 800*L2+280*L4
subject to
D{1}: L1+L2==1 ;
D{2}: L3+L4==1 ;
D{3}: 60*L2+28*L4<=80;
cvx_end
cvx reports the dual variables are:
[-200]
[ 0]
[ 10]
But is it obviously wrong!. The
correct dual variables are
[ 200]
[ 0]
[ 10]
you can solve it by hand. dual problem has 4 constraints and 3 dual variables.
Min y1+y2+80y3
y1>=0
y1+60y3>=800
y2>=0
y2+28y3>=280
CVX is not wrong. Unlike inequality constraints, the sign of the dual variable of an equality constraint (your first constraint) depends on convention, so either 200 or -200 could be correct. See Unexpected result .
It cause a real mess in dantzig-wolfe decomposition. How can i detect the real sign?
Just negate CVX’s output. Mark is correct, the sign of the equality constraints depends on convention. But CVX uses the same convention for equality constraints every time, so just change your code this once and be done.
Can you explain this case?
For the following LP
minimize x1+x2
subject to
D1:x1+x2<=5
D2:-x1+x2<=-2;
Cvx reports D1=0 and D2=1, but D2 must
be negative (-1) . Here is the Dual problem
maximize 5*D1-2*D2
subject to
x1:D1-D2<=1
x2:D1+D2<=1;
D1<=0;
D2<=0
Is it reports shadow price?
Inequality dual variables are always nonnegative in CVX. They represent the improvement in the objective with a unit relaxation in the inequality.
