I have an optimization problem as $$\min_x c(x)$$ $$ s.t. \quad \sum_i^n \alpha_ie^{-||x-y_i||^2/2l^2} \leq \beta$$
Here, $x\in \mathbb{R}^m$ is variable while $\alpha \in \mathbb{R}^n,\beta, l $ and $y \in \mathbb{R}^m$ are constants.
The obvious straightforward approach is to use nonlinear solver like fmincon. But I want to know is there any way to simplify this constraint to decrease its complexity.
Also, I understand that the problem is non-convex. But not being able to show how?
Is there any source talking about optimization problem of this kind?