Can this OP be solved in CVX?

I have a nonlinear optimization problem with linear constraints. How to solve this? \sigma_i and \rho_i are the optimization variables.


subject to



0<\rho_i\le c_i\hspace{1mm},i=1,2

\sigma_i\ge 0\hspace{1mm},i=1,2

\sigma_i=0,\hspace{1mm}\text{if }\rho_i=c_i\hspace{1mm},i=1,2



c_i and f_i, i=1,2 are positive and greater than 0.

Is it convex? Why isn't CVX accepting my model? READ THIS FIRST!

Ouch. the determinant of the Hessian of each D_i is negative. So each D_i is indefinite. So the problem is not convex.

It’s worse than that, the constraints aren’t even linear, there’s a logical component.