Hi all,

I wounder if I can solve this optimization problem through CVX ?

For a given values for t \in (1,...N) and P and the problem is

maximize \sum_{n=1}^{N} log det (X^{H}_{t}R_{n}X^{}_{t}+I_{t})

s.t. tr [X^{}_{t}X^{H}_{t}] \leq t P

Suppose we have different set of matrices R_{n}, where each R_{n} \in C^{N \times N} is a positive semidefinite, its diagonal elements are ones. Also each R_{n} is a rank deficient matrix.

I am expecting the output to be optimal matrix X_{opt}\in C^{N \times t}

Any ideas any hints. Many thanks.