&\text{ maximize } &\nu &\\
&\text{ subject to }& p &\in K&\\
& & \nu &\in \mathbb{R}&\\
&\text{ maximize } &\nu &\\
&\text{ subject to }& p &\in K&\\
& & \nu &\in \mathbb{R}&\\
&\text{ minimize } &\omega &\\
&\text{ subject to }& q &\in K&\\
& & \omega &\in \mathbb{R}&\\
&\text{ minimize } &\omega &\\
&\text{ subject to }& q &\in K&\\
& & \omega &\in \mathbb{R}&\\