Improved sequential optimality conditions for convex optimization problems with cone-epi-closed functions

Sequential optimality conditions are particularly interesting in optimization due to the fact that they do not require the fulfillment of any other constraint qualification, which is the case when working with other types of optimality conditions. In this article, we improve some previously published results for quite a general class of convex optimization problems, where the functions considered are cone-convex and cone-epi-closed, and then provide new sequential optimality conditions for convex composed optimization problems. They could be further used to deduce sequential characterizations for general classes of vector optimization problems.