A CONJUGATE DUALITY SCHEME GENERATING A NEW CLASS OF DIFFERENTIABLE DUALS

We construct a mechanism to generate a large class of duality schemes for (not necessarily differentiable) convex optimization problems, for which the dual problem is continuously differentiable. We use the con jugate duality framework of Rockafellar; the original primal problem i s embedded in a family of perturbed problems. The perturbation functio n is constructed in terms of two perturbation vectors and a single-var iable function q. The differentiability is a consequence of the dual o bjective function's being a kind of ''proximal regularization,'' but o ne which is expressed in terms of a nonquadratic regularizing term ass ociated with the function q.