I am trying to implement the following optimization (from this paper) in Matlab using fmincon:

$\min_\omega\omega'\Sigma\omega$ subject to $\min_Ur_p \geq r_0$ where $\Sigma$ is a positive definite matrix and $\omega$ is a vector of weights that sum to 1. The authors of the paper show that:

$\min_Ur_p=|\alpha||\omega|[cos(\phi)-\chi]$ where $\phi$ is the angle between the two vectors $\alpha$ and $\omega$ and $\chi$ lies between 0 and 1.

Any ideas how to implement this using matlab?