Consider the following convex problem $\max_{\mathbf{A}} \log |\mathbf{I} + \mathbf{CA} |$ subject to $\log |\mathbf{I} + \mathbf{FA} | \leq \xi$ where $\mathbf{A}$ is a semidefinite positive matrix and $\mathbf{I}$ is the identity matrix.

Does exist any closed form solution to $\mathbf{A}$? If not, does exist efficient algorithms to solve this problem?

Thanks in advance,

Mikitov

may beconcave, notisconcave. – Gilead Dec 25 '10 at 19:34