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?

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. Also, we have $r_p=\alpha'\omega$ and $U$ is the circle centred at $\alpha$ with radius equal to $|\chi|\alpha$ for $\chi$ between 0 and 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 $\omega$.

Any ideas how to implement this using matlab?

I am trying to implement the following optimization in Matlab using fmincon:

$\min_\omega\omega'\Sigma\omega$ subject to $\min_Ur_p$ where the authors show that:

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

Any ideas how to implement this using matlab?

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?