I have a problem formulated as:
$\underset{x,y}{\min} x^HAy$ subject to $\sum x = 1$ and $\sum y = 1$.
Where A is a complex matrix, and x and y are column vectors that I need to find.
This is very similar to the following convex optimization problem (e.g., minimum variance portofolio), $\underset{x}{\min} x^HAx$ subject to $\sum x = 1$, which has an analytical solution
$x = \frac{A^{-1} 1}{1^H A^{-1} 1} $, given that A is invertible. Does my problem have a similar solution? Or is there a technique to find the appropriate x and y via bilinear programming?