for the points $\r$ in the healthy region $\Omega_S$, the worst-case performance is rendered by the steering vectors which provide the highest power, whereas for the points $\r$ in the tumor region $\Omega_T$, those steering vectors which attain the lowest power are the ones which contribute in the worst-case performance. They are collectively referred to as the *worst steering vectors*. Therefore, for a given $\R$, either $\R_{nr}$ or $\R^\star$, the worst steering vectors for the control points $\r$ in $\Omega_S$ and $\Omega_T$, are obtained by maximizing and minimizing the transmit beampattern , respectively. Observe that finding the worst steering vectors for the points in the tumor region $\Omega_T$ equals solving the following convex minimization problem at each $\r \in \Omega_T$, i.e., $$\underset{\|\atil(\r)\|^2 \leq \epsilon}{\textrm{min}} \hspace{.2cm} (\ahat(\r) + \atil(\r))^H \R (\ahat(\r) + \atil(\r))$$ using `CVX` [@cvx2013; @gb08]. Whereas, for finding the worst steering vectors for the points in the healthy region $\Omega_S$, we obtain a local optimum for the following non-convex maximization problem at each $\r \in \Omega_S$, i.e., $$\underset{\|\atil(\r)\|^2 \leq \epsilon}{\textrm{max}} \hspace{.2cm} (\ahat(\r) + \atil(\r))^H \R (\ahat(\r) + \atil(\r)),$$ using semidefinite relaxation techniques from [@Beck06strongduality].

We evaluate the designed beampatterns plotting the spatial power distribution in decibel scale, i.e., $20 