Yes, that is SCA, used to (attempt to solve a non-convex problem by solving a sequence of convex optimization problems, plus in your case, problems which can be solved analytically.
If you use Mosek or CVXQUAD, the solution to the CVX problems might be changed enough, even if very little, that somehow the overall algorithm works for some particular input data, but that would just be luck, and might not apply more generally.
The bottom line is that many of the SCA and similar algorithms published in Electrical Engineering journals are non-robust junk, which can’t reliably be applied to new input data sets. Don’t blame me, because I have not been an advisor, editor, or referee on any of them.
Thank you very much for your answers, I will try to use YALMIP non convex solver as you suggested before. See what can it do.
And by the way, can I know what is your normally active/online time range? Thank you.
And could you please share me the link about the YALMIP non convex solver, I saw a " Nonconvex quadratic programming" I’m not sure if that is the right one or not, thank you.
YALMIP is an optimization modeling system which handles convex and non-convex optimization. It is not a solver per se; it needs to call a solver. But it does include some of its own solvers, such as BMIBNB for non-convex global optimization, but that in turn may need to call others solvers, such as FMINCON or a Mixed_Integer Linear Programming solver.