How to solve my optimization problem? \begin{equation} \min_{\mathbf{p}}\ \ \log \{(2\pi e)^M\det(\mathbf{R_p})\}\\ \text{s.t.} \ \ \ \ \|\mathbf{p}\| \leq s \end{equation} where $\mathbf{p}\in \mathbb{R}^M$ is a binary vector taken from {0,1}. $\mathbf{R_p}=\Phi_{\mathbf{p}} \mathbf{R}\Phi_{\mathbf{p}}^T$ can be obtained from the covariance matrix $\mathbf{R}$ by removing the rows or columns corresponding to $p_i=0,\forall i$. And $\mathbf{R}$ is an $\mathbb{R}^{M\times M}$ matrix, $\Phi_{\mathbf{p}} \in \mathbb{R}^{\|\mathbf{p}\|_0 \times M}$ is the matrix by removing the all-zeros columns of $\text{diag}(\mathbf{p})$.
Who can tell me a trick? Thanks a lot.