Dualities for non-Euclidean smoothness and strong convexity under the light of generalized conjugacy

Abstract

Relative Bregman smoothness and strong convexity have recently gained considerable attention in optimization. However, conjugate dualities for Bregman smoothness and strong convexity remain an open problem as noted earlier by Lu, Freund, and Nesterov, Relatively smooth convex optimization by first-order methods, and applications,