Dual Variable Calculation

1

Dear Friends
I have the following LP problem:

cvx_clear;
clear all;
cvx_solver gurobi;
input=[0;2];
M=[20 20];
c=[-1 1];
cvx_begin
    variable x(2) nonnegative;
    variable y(2) nonnegative;
    variable u(2) nonnegative;
    dual variable D1;
    dual variable D2;
    
    minimize c*y+ M*u
subject to      
    2*y(1)-u(1)<=12-3*x(1);
    y(2)-u(2)<=-18+6*x(2);
      D1 : x(1)==input(1);
      D2 : x(2)==input(2);
cvx_end

When I change solver to the Mosek, I got the following result:
D1=0 D2=-120
and its correct.

When I change solver to the Guobi, I got the following result:
D1=1.5 D2=-120
and its wrong.

When I change solver to the SDPT3 v4.0, I got the following result:
D1=-61.9453 D2=-120
and its wrong.

I think this is a bug!

2

Why do you think it is a bug?

It could very well be that the dual problem does not have a unique optimal solution and all the dual solutions you see are optimal.

I suggest you check wether the dual solutions are feasible and if they have the correct optimal objective value. If not you have proved there is a bug somewhere.