There is a variable x(2,2) complex

I want to use x*x’ in my function.
I only found sum_square_abs(x) to get the diagonal of x*x’.

It seems like there is no way to have the full x*x’

Any reformulation to get it out?

Thank you.

There is a variable x(2,2) complex

I want to use x*x’ in my function.
I only found sum_square_abs(x) to get the diagonal of x*x’.

It seems like there is no way to have the full x*x’

Any reformulation to get it out?

Thank you.

1 Like

Please provide a context for what you want to do. Is your problem actually convex, and if so, how have you determined that? This question will be marked non-convex, unless and until you show you are trying to do something convex.

I don’t have the context with me right now,I will try to prove it later

maybe I could simplify my question.

Can I run it somehow?

```
cvx_begin
variable x(2,2)
expression y
y=x*x'; %this is not allowed.is that means a matrix multiply its own transpose is an Nonconvex expression?
maximize y
subject to
x(:)<=1
cvx_end
```

Forget about convexity or DCP rules for the moment. Your program doesn’t make any sense. Your objective function is a 2 by 2 matrix. Your objective function needs to be a real scalar. If you show us what your objective function really is, perhaps further advice can be provided.

Sorry，my mistake.

I will provide my object function next week.

I’m currently facing this problem too, I’m working on my senior thesis on radar signal processing topic. The process appears similar to A*X*X’*A’ (A is a known matrix). I have provided the diagram below to specifically illustrate my problem, where F_BB is the unknown variable in the equation. Is there a specific code to solve X*X’, or I need to convert it? Could you give me some advice on this issue?

If you defined a new variable (variables?) consisting of F_{BB}F_{BB}^H, which would be declared as hemitian_semidefinite, and presuming \lambda_{i,j} \ge 0, then the argument of log_det would be affine henmitian semidefinite, so R would be the sum of `log_det/(...)/log(2)`

But that would only be viable if F_{BB} is not needed by itself elsewhere in your problem.

Perhaps someone else has a better idea. Is there a determinantal identity which can be used?

But in any event, have you proven your optimization problem is convex?

This is neither convex nor concave in terms of the variable F_{BB}, although it is concave in terms of F_{BB}F_{BB}^H (if \lambda_{i,j} \ge 0).

That is because in the scalar case, `log(1+x^2)`

is convex (in terms of x) for x^2 \le 1, and concave for x^2 \ge 1. Hence it is neither convex nor concave in terms of x.