Solving DIMACS 7 problems using MOSEK and YALMIP

Question

I'm trying to test the MOSEK solver in the YALMIP MATLAB environment to try and solve a DIMACS 7 problem, but am having some issues. In particular, I'm trying to solve the "sched_50_50_orig" problem given near the bottom of the following link: http://dimacs.rutgers.edu/Challenges/Seventh/Instances/. The following MATLAB code is used to solve the problem once the sched_50_50_orig.mat file has been loaded into MATLAB's memory,

options = sdpsettings('solver','mosek','verbose',1);
m = 4979;
x = sdpvar(m,1);

objective = c'*x;
constraints = [A*x == b];

optimize(constraints,objective,options);
x_opt = value(x);

Unfortunately, the above code gives me a primal infeasibility error instead of finding the optimal solution of 26673 given in the following link: http://dimacs.rutgers.edu/Challenges/Seventh/Instances/tablestat.html. Any help as to what I'm doing wrong would be much appreciated, thanks very much.

Answer 1

What Yalmip passes to Mosek is actually the dual problem. So what you see as Primal Infeasible status in Mosek log is actually a Dual Infeasible (i.e. unbounded) for the original problem. It is unbounded because you did not include the conic constraint, only the linear ones.

The actual representation of this problem is

objective = c'*x;
constraints = [A*x == b; x(1:2502) >= 0; cone(x(2504:2504+2472), x(2503)); cone(x(4978:4979), x(4977))];

and then is solves ok I think.