Decentralized Constrained Optimization: Double Averaging and Gradient Projection

Firooz Shahriari-Mehr, David Bosch, Ashkan Panahi

Abstract: In this paper, we consider the convex, finite-sum minimization problem with explicit convex constraints over strongly connected directed graphs. The constraint is an intersection of several convex sets each being known to only one node. To solve this problem, we propose a novel decentralized projected gradient scheme based on local averaging and prove its convergence using only local functions’ smoothness. Experimental studies demonstrate the effectiveness of the proposed method in both constrained and unconstrained problems.