Warning: mosek does not support semidefinite constraints

[mk2510]

Hi,

I tried to implement the SDP relaxation 6 from this paper, with a variation, that it should operate on 2 graphs at the same time, so I basically just doubled all variables and constraints.
I came up with the following code:

problem.yy = sdpvar(params.n, 1, 'full');
X = problem.X;
yy = problem.yy;
A1 = problem.P{1};
A2 = problem.Q{1} * X;
[a,b] = size(A1);
one = ones(a,1);
sp1 = one' * A1 * (one + yy)/2;
sp2 = one' * A2 * (one + yy)/2;
sm1 = one' * A1 * (one - yy)/2;
sm2 = one' * A2 * (one - yy)/2;
s1 = one' * A1 * one;
s2 = one' * A2 * one;
gamma = yy * yy';
d1 = A1 * one;
d2 = A2 * one;
D1 = diag(d1);
D2 = diag(d2);
p1 = 4*sp1*sm1 / (s1*s1);
p2 = 4*sp2*sm2 / (s2*s2);
 
obj = 1/p1 * trace(gamma*((D1-A1)/s1)) + 1/p2 * trace(gamma*((D2-A2)/s2));
 
%(gamma >= 0) don't think I need this constraint, as y*y' has entries >= 0
constraints = [ (diag(gamma)== one) 1/(s1*s1)*trace(gamma * d1 * d1') == 1-p1 ...
    1/(s2*s2)*trace(gamma* d2 * d2') == 1-p2 p1>0 p1<=1 p2>0 p2<=1];

My problem now is, that I get the following warning: Warning: Solver not applicable (mosek does not support semidefinite constraints)

Could you please help me understand, what I did wrong, to produce this warning?

[johanlofberg]

I think you are running some old broken develop version

[johanlofberg]

It also looks like you've misunderstood the whole idea with a semidefinite relaxation, as you introduce a quadratic inner product yy'. The idea in (lowest-order) semidefinite relaxations is that you express the model in yy' and then replace that with a matrix Y with the constraint that Y >=0 and Y has rank 1, and then you drop the rank constraint.

In your case, it means you want gamma = sdpvar(params.n) and gamma >=0

As you have it now, you have a nonlinear nonconvex semidefinite program, much harder than the original nonconvex quadratic program you probably started with

[mk2510]

Thanks a lot for your help. When I implemented the full relaxation I got rid of those error messages.

[johanlofberg]

Not sure what you mean with full relaxation, as what you did was not a relaxation at all, but good that it was fixed.

Note also that all these things can be done automatically for you with the moment relaxation framework