An Interior-Point Lagrangian Decomposition Method for Separable Convex Optimization

TL;DR

This paper introduces a distributed interior-point method leveraging Lagrangian dual decomposition and self-concordant barriers to efficiently solve large-scale separable convex optimization problems with proven global convergence.

Contribution

It presents a novel interior-point Lagrangian decomposition algorithm that ensures self-concordance and parallelizability for large-scale convex problems.

Findings

Algorithm is globally convergent.

Method is highly parallelizable.

Effective for large-scale problems.

Abstract

In this paper, we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian, we prove under mild assumptions that the corresponding family of augmented dual functions is self-concordant. This makes it possible to efficiently use the Newton method for tracing the central path. We show that the new algorithm is globally convergent and highly parallelizable and thus it is suitable for solving large-scale separable convex problems.