In the study of a non-convex minimization problem by Lachand-Robert and Peletier, they found that the difference between the compactly supported perturbation $u+εh$ of a strictly convex function $u$, and the $Γ$-regularization of $u+εh$, is at most $o(ε)$. Here we find that this result is optimal, albeit they expected a much stronger estimate.