Problem about nuclear minimization

1

I use Mosek to solve this nuclear minimization problem, but it returned “error”, could someone tell me why?

matlab code:-------------------------------------------
function [W]=mysolve_sdp(A,c,A0,t0)

n=156;

cvx_begin
variable X(n+1,n+1) symmetric
minimize (norm_nuc(X));
subject to
for i=1:260
trace(A(:,:,i)*X) <= c(i);
end
for i=261:403
trace(A(:,:,i)*X)==c(i);
end
X==semidefinite(n+1);
diag(X)==ones(n+1,1);
cvx_end
W=X;
end

2

What is the error exactly?

3

It says no enough space.

By the way I have only seen min-nuclear norm problem with equality constraints, is such nuclear norm minimizing problem with inequality constraints solvable?

4

Not enough space means it ran out of memory. You can have all kinds of linear constraints you want. Can you post full log output from the solve?

5

Inequality constraints are fine, provided they are convex, and satisfy CVX’s (DCP) rules. What is allowed for these constraints is no different than if norm(…,2), norm(…,1), or norm(;;;,inf) were used instead of norm_nuc .