How to convert this constraint into a convex constraint

1

QQ截图20241023144801
In this constraint, A is optimization matrix (dimension is K*N) needed to be optimized, c is a constant and the norm is F norm. It seems nonconvex, so how to convert this constraint into its convex form using SCA?

2

Here is pseudo-code for SCA. You should add error handling in case a CVX problem is not solved. A_old is not declared as a CVX variable. It is data input to the CVX problems.

It might not converge at all. If it does converge, it might to be to some value other than a local optimum of the original problem, let alone a global optimum. The stating value for A_old may strongly affect what happens.

A_old = starting_value;
while not converged up to maximum number of iterations
  cvx_begin
  variable A
  % the rest of the CVX code, including other variable declarations
  norm(A*A_old,'fro') <= c
  cvx_end
  A_old = A;
end