Abstract:

We first introduced the dual schemes for a composed convex optimization problem. Then, using the properties of subdifferential, we introduced a new MoreauRockafellar formula for a composed convex function. And using the MoreauRockafellar formula, we obtained some necessary and sufficient conditions which characterize the stable total duality for the composed convex optimization problem.

Key words: composed convex optimization problem, MoreauRockafellar formula, stable total duality, total duality