Greater than equal restriction on CVX

Nonconvex
1

Hello i am on the develop of an algorithm that allows the voltage regultation, when i try to delimit the minimum and maximum allowed values i have a litte problem.

% optimizacion
cvx_solver SeDuMi
cvx_precision high
cvx_begin quiet
variable Vn(MG.NumN*3-3) complex;
variable Si(MG.NumS) complex;
variable perdidas;
variable Valor_Esperado;
variable xi(MG.NumS);
minimize Valor_Esperado;

subject to

        Valor_Esperado == perdidas;
        quad_form(Vn(:),YNN)+real(Vn(:)'*YN0*v0)+real(v0'*conj(YN0')*Vn(:))+ real(v0'*Y00*v0) <= perdidas;         
        (Dg*Si(:)+Spn)== H*conj(Vn(:)) + M*Vn(:) + T;  
        abs(Si(:)) <= abs(Smax);
        real(Si(:))>= 0;
        real(Si(:)) == real(Smax);
        imag(Si(:)) <= imag(Smax);
        imag(Si(:)) ==  xi.*imag(Smax);
        abs(Vn(:))<= 1.05;
        if real(Smax)<=0.3*imag(Smax)
                imag(Si(:))==-imag(Smax)
        else
            imag(Si(:)) ==  xi.*imag(Smax);
            abs(Vn(:))<= 1.05;
            xi >= -1
            xi <= 1; 
        end  
      cvx_end

the problem appears when i want to define the lower bound abs(Vn(:))>=0.95, the optimization model works without and with the upper bound, but not with it.

theres any form to redefine the abs(Vn(:))>=0.95 in a way that the bound got define on the model and still work on CVX

2

abs(Vn(:))>=0.95 is a non-convex constraint.

if Vn were real,it could be modeled in CVX using Big M logic constraints, as shown in section 9.1.6 “Exact absolute value” of the Mosek Modeling Cookbook

However, I am not aware of any way of using binary or integer variables to handle abs(complex variable).