I am working on convex approximations for non-convex optimization problems. For a non-convex constraint $g(x) \leq 0$ with Lipschitz continuous gradient i.e. ($\lvert|\nabla g (x_{1})-\nabla g(x_{2})\rvert|\leq L \lvert| x_{1}-x_{2}\rvert|$), a quadratic upper bound is given by $g(y)+\nabla g(y)(x-y)+\frac{L}{2}\lvert|{x-y}\rvert|^2$.
Is there a way to estimate the value of this Lipschitz constant?