How to convexify (relax) this L0 eigenvalue optimization problem?

Question

Let $C_1,\dots,C_L$ be $N\times N$ hermitian matrices. Let $d<0$ be a given negative constant. Then consider the optimization problem \begin{align} \max_{r\in \mathcal{R}^{L\times 1}} &\mid\mid r\mid\mid_0 \\ \mbox{subject.to.} ~~~~~~&~~\lambda_{min}\left(\sum_{i}r_iC_i\right)\leq d \\ ~&~~\sum_ir_i=1,~~r\geq 0 \end{align}