Feasible problem is unfeasible

[Fabio Paparella]

This is a the problem I'm trying to solve.

I also attached a .m version

x = binvar(5,5,2)

toll=10e-5;

constraints = [];

constraints = [constraints

     sum(sum(x,3),1)' >= [0; 1; 0; 1; 1] - toll;

     sum(sum(x,3),1)' <= [0; 1; 0; 1; 1] + toll;

     sum(sum(x,3),2)  >= [1; 0; 1; 0; 1] - toll;

     sum(sum(x,3),2)  <= [1; 0; 1; 0; 1] + toll;

     ];

 

 objective = sum(sum(ones(5,5).*sum(x,3))) 

 

 options = sdpsettings('verbose',1,'solver','gurobi');

option.gurobi.QCPDual = 1;

sol4 = optimize(constraints,objective,options);

This is a solution I found analytically.

If I substitute the solution I found, every constraint is satisfied, but the solver says it is unfeasible.

I also added tolerances (transformed 2 equality constraints in 4 inequalities)

Can you help me??

solution(:,:,1)=[

     0     0     0     0     0;

     0     0     0     0     0;

     0     0     0     1     0;

     0     0     0     0     0;

     0     0     0     0     0

];

solution(:,:,2) =[

     0     0     0     0     1;

     0     0     0     0     0;

     0     0     0     0     0;

     0     0     0     0     0;

     0     1     0     0     0

     ];

Best,

Fabio

[Johan Löfberg]

You are constraining x to be symmetic as that is default

https://yalmip.github.io/tutorial/basics/