Considering the convex optimization problem min {f(x)∣,gi(x)≦0,i=1, …,n} we call a smooth convex functionGa convex smoothing, if{x∣G(x)≦0} includes the feasible set, and if the resulting problem min{f(x) ∣G(x≦0)} is equivalent to the initial problem. A relation is developed to the Lagrangian functions: with the involved multiplier functions we are able to define such convex smoothings in some cases.