The q‐asymptotic function is a new tool that permits to study nonconvex optimization problems with unbounded data. It is particularly useful when dealing with quasiconvex functions. In this paper, we obtain formulas for the q‐asymptotic function via c‐conjugates, directional derivatives and subdifferentials. We obtain them under lower semicontinuity or local Lipschitz assumptions. The well‐known formulas for the asymptotic function in the convex case are consequences of these ones. We obtain a new formula for the convex case.
