The analytic center cutting plane method and its proximal variant are well known techniques for solving convex programming problems. We propose two sequential convex programming variants based on convexification techniques for nonconvex unconstrained problems. The performance of the algorithm is compared with that of two other well known first-order algorithms, the steepest descent and nonlinear conjugate gradient with Armijo line search on a set of 158 problem from the CUTEr test set.