Accelerated Primal Dual Method for a Class of Saddle Point Problem with Strongly Convex Component

Abstract

This paper presents a simple primal dual method named DPD which is a flexible framework for a class of saddle point problem with or without strongly convex component. The presented method has linearized version named LDPD and exact version EDPD. Each iteration of DPD updates sequentially the dual and primal variable via simple proximal mapping and refines the dual variable via extrapolation. Convergence analysis with smooth or strongly convex primal component recovers previous state-of-the-art results, and that with strongly convex dual component attains full acceleration $O(1/k^2)$ in terms of primal dual gap. Total variation image deblurring on Gaussian noisy or Salt-Pepper noisy image demonstrate the effectiveness of the full acceleration by imposing the strongly convexity on dual component.