## Covering Number of a Positive Semidefinite Cone (Approximate the Objective of a SDP)

I was wondering what the covering number of a positive semidefinite cone is. Consider the semidefinite optimization program \begin{align} \max\langle \mathbf{C}, \mathbf{X} \rangle~~\text{subject to}~~ \langle \mathbf{A}_i, \mathbf{X} \rangle \leq b_i, i= 1,\ldots, m, \mathbf{X} \succeq \mathbf{0}. \end{align} Is it possible to find finite number of elements $\{ \mathbf{V}_k \}_{k=1}^N$ in the SDP cone \begin{align} \left\{ … Read more