I have an optimization problem with bilinear constraint, as follows
\begin{align} \min_{x,s,\lambda} \quad J(x)\\ f(x)=0\\ \lambda^\top x+h(\lambda,x) \leq s\\ \lambda^\top e=1\\ \lambda\geq 0\\ g(\lambda,x)\leq0 \end{align}
where $x \in \mathcal{X} \subset \mathbb{R}^n$, $s \in \mathbb{R}$, $\mathcal{X}$ is a convex set, $e$ is a vector consisting of all ones. In addition, $J(x)$ is a quadratic function, $f(x)$ and $h(\lambda,x)$ are affine functions, $g(\lambda,x)$ is a convex function.
The above optimization problem is nonconvex because of the second constraint. I've tried McCornick relaxation, but it yields to a very loose relaxation.
Is there any way to handle the above problem?