Consider three $N \times N$ hermitian matrices $A_0,A_1,A_2$. Consider the function \begin{align} f(t_1,t_2)=\lambda_{min}(A_0+t_1A_1+t_2A_2) \end{align} where $\lambda_{min}$ denotes the minimum eigen-value. $f(t_1,t_2)$ is clearly a concave function. How do we find the sub-gradient of it?