ﻻ يوجد ملخص باللغة العربية
In this work, we introduce ADAPD, $textbf{A}$ $textbf{D}$ecentr$textbf{A}$lized $textbf{P}$rimal-$textbf{D}$ual algorithmic framework for solving non-convex and smooth consensus optimization problems over a network of distributed agents. ADAPD makes use of an inexact ADMM-type update. During each iteration, each agent first inexactly solves a local strongly convex subproblem and then performs a neighbor communication while updating a set of dual variables. Two variations to ADAPD are presented. The variants allow agents to balance the communication and computation workload while they collaboratively solve the consensus optimization problem. The optimal convergence rate for non-convex and smooth consensus optimization problems is established; namely, ADAPD achieves $varepsilon$-stationarity in $mathcal{O}(varepsilon^{-1})$ iterations. Numerical experiments demonstrate the superiority of ADAPD over several existing decentralized methods.
This paper investigates accelerating the convergence of distributed optimization algorithms on non-convex problems. We propose a distributed primal-dual stochastic gradient descent~(SGD) equipped with powerball method to accelerate. We show that the
We introduce a novel primal-dual flow for affine constrained convex optimization problem. As a modification of the standard saddle-point system, our primal-dual flow is proved to possesses the exponential decay property, in terms of a tailored Lyapun
This paper considers a general convex constrained problem setting where functions are not assumed to be differentiable nor Lipschitz continuous. Our motivation is in finding a simple first-order method for solving a wide range of convex optimization
We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for all classes
We propose a new majorization-minimization (MM) method for non-smooth and non-convex programs, which is general enough to include the existing MM methods. Besides the local majorization condition, we only require that the difference between the direc