Distributed and Asynchronous Algorithms for N-block Convex Optimization with Coupling Constraints

TL;DR

This paper introduces distributed asynchronous algorithms for N-block convex optimization with coupling constraints, demonstrating convergence and efficiency improvements over synchronous methods.

Contribution

It proposes an N-block PCPM algorithm with proven global convergence and a novel asynchronous variant with sub-linear convergence under bounded delays.

Findings

Linear convergence rate under strong second-order conditions

Faster convergence with more short-time iterations

Effective asynchronous algorithm under bounded delay

Abstract

This paper first proposes an N-block PCPM algorithm to solve N-block convex optimization problems with both linear and nonlinear constraints, with global convergence established. A linear convergence rate under the strong second-order conditions for optimality is observed in the numerical experiments. Next, for a starting point, an asynchronous N-block PCPM algorithm is proposed to solve linearly constrained N-block convex optimization problems. The numerical results demonstrate the sub-linear convergence rate under the bounded delay assumption, as well as the faster convergence with more short-time iterations than a synchronous iterative scheme.