On Primal-Dual Stability in Convex Optimization

Conditions are given ensuring the stability of the classical duality scheme of Ekeland-Temam-Rockafellar with respect to the slice topology (a generalization of the Mosco topology to the non reflexive setting). Both primal and dual aspect are tackled allowing convergence of primal solutions along with the Lagrange multipliers. An example of application is given to optimal control of distributed parameter systems.