Element Wise Division in Inequality Constraints ( Not solvable by CVX. Cause DCP Error)

Hi All,

I want to solve a minimization problem, which has element wise division as constraints. I have tried to use CVX but the CVX caused DCP (Disciplined Convex Programming) error. Although, the constraint is convex.

min ||x||_1 such that norm((y-Ax)./sqrt(Ax), 2) \leq \epsilon and x>0 and Ax>0

./ is element wise division.


To me it seems something along the lines

\begin{array}{rcl} (y-Ax)_j^2 & \leq & u_j v_j, \quad u_j,v_j \geq 0, \\ Ax-u & = & 0, \\ ||t|| & \leq & \epsilon \\ x & \geq & 0 \\ \end{array}

would work. The first constraint is a Lorentz cone.

Btw you cannot do x strictly greater than 0.