I have a model which looks like
$$ f(\mathbf{x}) = \sum_{i=1}^N\lambda_i\exp\left[-\frac{1}{2}(\mathbf{x} - \mathbf{\mu}_i)^T \Sigma^{-1} (\mathbf{x} - \mathbf{\mu}_i)\right] $$
The $\Sigma$ is symmetric and positive semi-definite covariance matrix, and all the squared-exponential functions have same $\Sigma$ matrix.
Now, I want to make sure that $\forall x \in R^d, f(\mathbf{x}) \geq 0$, what constraints should I pose to all the $\lambda_i$?
Posing constraints that all $\lambda_i > 0$ of course works, but that may make my model perform poorly, to make the model accurate, some $\lambda_i$ shoule be less than zero, so, can I further relax the constraints?