I am trying to find a closed-form solution to an interesting optimization problem, which seems to be simple, but not trivial in fact. OK, here is the problem:
min$_s$ Re($v^Hs$)
s.t. $||s||_2=1$, $s^HAs\le\epsilon$,
where Re($\cdot$) denotes the real part of a complex number, and $A$ is a positive definite matrix. The value of $\epsilon$ is between the small eigenvalue and the largest eigenvalue of $A$.
I am looking forward that someone can help me!!!!