A unified convergence rate analysis of the accelerated smoothed gap reduction algorithm

In this paper, we develop a unified convergence analysis framework for the Accelerated Smoothed GAp ReDuction algorithm (ASGARD) introduced in Tran-Dinh et al. (SIAM J Optim 28(1):96–134, 2018). Unlike 2018), new covers three settings single algorithm: general convexity, strong and convexity smoothness. Moreover, establish guarantees on criteria: (i) gap function, (ii) primal objective residual, (iii) dual residual. Our rates are optimal (up to constant factor) all cases. While rate residual convex case has been established prove additional function The last two cases is completely new. results provide complete picture of ASGARD. Finally, present four different numerical experiments representative optimization model verify our compare it with well-known Nesterov’s smoothing algorithm.