Minimizing quadratic objective function on the unit $\ell_1$ sphere I would like to solve the following optimization problem using a quadratic programming solver
$$\begin{array}{ll} \text{minimize} & \dfrac{1}{2} x^T Q x + f^T x\\ \text{subject to} & \displaystyle\sum_{i=1}^{n} |x| = 1\end{array}$$
How can I re-write the problem using linear constraints?
Note: I have read other similar questions. However, they define the absolute value differently. 

This is not possible. The set
$$\{x \in \mathbb R^n \mid \sum_{i=1}^n |x_i| = 1\}$$
is not convex, but the feasible set of a quadratic program is convex.
