This paper presents the theory that guarantees the convexification of a strictly monotone function. We proves a theorem and two corollaries for convexification of strictly monotones functions twice continuously differentiable, then the generalization of these results is presented for convexication of nondifferentiable strictly monotones functions. Both cases are exemplars. This results are using in optimization nonsmooth.

This paper presents the theory that guarantees the convexification of a strictly monotone function. We proves a theorem and two corollaries for convexification of strictly monotones functions twice continuously differentiable, then the generalization of these results is presented for convexication of nondifferentiable strictly monotones functions. Both cases are exemplars. This results are using in optimization nonsmooth.