&\text{ maximize } &\nu &\\
&\text{ subject to }& p &\in K&\\
& & \nu &\in \mathbb{R}&\\
- & & \left\langle p,e_{1} \right\rangle &= 1&\\
+ & & \left\langle p,e_{2} \right\rangle &= 1&\\
& & L\left(p\right) &\succcurlyeq \nu e_{1}.&
\end{aligned}
&\text{ minimize } &\omega &\\
&\text{ subject to }& q &\in K&\\
& & \omega &\in \mathbb{R}&\\
- & & \left\langle q,e_{2} \right\rangle &= 1&\\
+ & & \left\langle q,e_{1} \right\rangle &= 1&\\
& & L^{*}\left(q\right) &\preccurlyeq \omega e_{2}.&
\end{aligned}