I Know that the problem isn’t convex but it is a quasi-convex

[References]
[1] Haitham Hindi, "A Tutorial on Convex optimization", In American Control Conference, Boston, USA, June 2004
----> page 12
[2] Constantinos Skarakis, CONVEX OPTIMIZATION theory and practice, M.Sc. Thesis
http://maths.york.ac.uk/www/sites/default/files/Skarakis.pdf
---> page 59

My original problem is

max min (Xi/Yi) % i = 1,2
subject to
sum_square_abs(alphas'*Pow1_R)<= Psum;

And from Boyd Book (Convex optimization):
The General Fractional programing form is :

minimize max(Xi/Yi)

which is a quasi-convex that could be converted to convex form by using bisection as:

minimize gamma
subject to
Yi > o % i=1,2
Xi <= gamma * Yi % i=1,2
% add original constraints
sum_square_abs(alphas'*Pow1_R)<= Psum;

But since my original problem is maximizing the minimum, i use the form:

minimize max(- Xi/Yi)
subject to
Yi >= 0
-Xi <= gamma * Yi
sum_square_abs(alphas'*Pow1_R)<= Psum;

I want to know if their is a condition for the quasi-convex function to be used in this manipulation or their are any steps i didn’t do it right

CVX does not handle quasiconvex problems natively. You will have to build your own iterative solver that converts the quasiconvex problem to a sequence of convex feasibility problems. But the feasibility problem as you have stated it is not convex, either.

To be honest I simply am not convinced that your original problem is quasiconvex. In order for that to be the case the fixed feasibility problems would themselves have to be convex, and it is quite clear that your model above is not.