I am trying to find the sum of 2 smallest eigenvalues using CVX.

I know you would say it is not a convex problem. but if you consider the

hypograph of the problem then it is convex problem and the maximizing it

would be ok.

I have the following model. B is incidence matrix, L is Laplacian matrix,

```
n = 8;
k = 2;
B = [ 1 0 0 1 0 0 0 0 0 0 0 0 0;
-1 1 0 0 1 1 0 0 0 0 0 0 1;
0 -1 1 0 0 0 0 0 -1 0 0 0 0;
0 0 -1 0 0 -1 0 0 0 -1 0 0 0;
0 0 0 -1 0 0 -1 1 0 0 0 0 0;
0 0 0 0 0 0 1 0 0 0 1 0 0;
0 0 0 0 0 0 0 -1 1 0 -1 1 -1;
0 0 0 0 -1 0 0 0 0 1 0 -1 0];
L = B *B';
cvx_begin sdp
variable Z(n,n) symmetric
variables lambda mu
maximize (k * lambda + trace(eye(n) * Z))
subject to
L - lambda * eye(n) - Z - mu * ones(n,n) == semidefinite(n);
Z == semidefinite(n);
cvx_end
```

It is unbounded(+Inf), But as someone can say it has to have 2.8860 solution. Because by finding eigenvalues separately you get this.