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.

  • $\begingroup$ Can you specify if $v_i$ is a vector? If so, does it have unit modulus $|v_i\cdot v_i| ^2=1$ (is it a pure quantum state)? It would be nice if you can talk about the background motivation of the question: e.g. a quantum mechanical problem. $\endgroup$ – Juan Bermejo Vega Dec 9 '15 at 16:30

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