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;

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;

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

What is the error exactly?

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?

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?

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 .