ɛ-Optimality conditions for composed convex optimization problems

The aim of the present paper is to provide a formula for the ɛ-subdifferential of f+g∘h different from the ones which can be found in the existent literature. Further we equivalently characterize this formula by using a so-called closedness type regularity condition expressed by means of the epigraphs of the conjugates of the functions involved. Even more, using the ɛ-subdifferential formula we are able to derive necessary and sufficient conditions for the ɛ-optimal solutions of composed convex optimization problems.