How to avoid the solution result being 0 or sparse?

1

When I use cvx to solve SDP problem, how to avoid the solution result being 0 or sparse?
How to add constraint R>0, where R is a complex hermitian toeplitz matrix?
Thanks!

2

You need to provide more specific information about your problem.

What do you mean by R > 0? is that a semidefinite constraint? if so, use
R >= small_positive_number*eye(n) if in sdp mode, or
R - small_positive_number*eye(n) == semidefinite(n) if not in sdp mode. small_positive_number is perhaps 1e-4 or 1e-5.

3

If i use R >= small_positive_number*eye(n), it will report error “Disciplined convex programming error:
Invalid constraint: {complex affine} >= {constant}”.

4

That is for sdp mode. Use ... == semidefinite… if not in sdp mode.

If you actually want elmentwise inequality, then you will have to use real(...) >= 0 and/or imag(...) >= 0 or whatever it is that you want.

5

But if I use … == semidefinite…, the elements of solution result will be 0 or sparse.

6

By that, I meant
R - small_positive_number*eye(n) == semidefinite(n)

Note I corrected a typo in my previous post where I had == 0 instead of ` == semidefinite(n)``

Or use the … >= 0 if using sdp mode.

Because I have no idea what your problem is, I don’t know whether this will resolve matters for you.