Given matrices ${\bf A} \in \mathbb R^{m \times n}$ and ${\bf B} \in \mathbb R^{p \times n}$ and scalar $c \in \mathbb R$,
$$\begin{aligned} &\underset{{\bf x}, {\bf y} \in \mathbb R^n}{\text{minimize}} & & {\bf x}^\top {\bf y} \\ &\text{subject to}& & {\bf A} {\bf y} \preceq {\bf 0}_m, \quad \| {\bf B} {\bf x} \|_2 \leq c \\ \end{aligned}$$
What makes this problem non-convex is that fact that both variables $\bf x$ and $\bf y$ are multiplied together in the objective. I am looking for suggestions and resources to tackle the non-convex optimization problem above, which I came across at work. Any help is appreciated.
Motivation
This is a problem in transportation flow optimization, where $\bf x$ are the returns and $\bf y$ are the desired weights. The objective is to maximize the total return subject to linear constraints on weights and a norm constraint on the returns vector.