I have a constrainted optimization problem in the Von Neumann Entropy.
In a CVX-like syntax the problem goes as follows: given variable $\mathtt{c(n)}$ $$\begin{align} \text{minimize} \qquad & S(A)=\mathrm{trace}\left(A log(A)\right)\\ \text{subject to} \qquad & A = \sum_i^n c_i v_i v_i^T\\ & \sum_i^n c_i = 1\\ & c_i \ge 0 & i=1,...,n\end{align} $$.
Does someone know how to solve this efficiently? I already know it probably cannot be cast as an SDP problem. If someone knows how to calculate the Von Neumann Entropy itself efficiently, it would also be helpful.