Sequential Optimality Conditions in Convex Programming via Perturbation Approach

A necessary and sufficient sequential optimality condition without a constraint qualification for a general convex optimization problem is given in terms of the ε-subdifferential. Further, a sequential characterization of optimal solutions involving the convex subdifferential is derived using a version of the Bröndsted-Rockafellar Theorem. We prove that some results from the literature concerning sequential generalizations of the Pshenichnyi-Rockafellar Lemma are obtained as particular cases of our results. Moreover, by this general approach we succeed to improve some sequential Lagrange multiplier conditions given in the past.