A Distributed Algorithm for High-Dimension Convex Quadratically Constrained Quadratic Programs

TL;DR

This paper introduces a distributed Jacobi-style algorithm for solving large-scale convex QCQPs, enabling parallel computation and data distribution, with proven convergence and demonstrated scalability on computer clusters.

Contribution

A novel predictor-corrector primal-dual distributed algorithm for large convex QCQPs, addressing scalability and data distribution challenges.

Findings

Algorithm converges to a global optimum under certain conditions.

Demonstrates favorable scalability on large datasets.

Effective implementation on a multi-node MPI cluster.

Abstract

We propose a Jacobi-style distributed algorithm to solve convex, quadratically constrained quadratic programs (QCQPs), which arise from a broad range of applications. While small to medium-sized convex QCQPs can be solved efficiently by interior-point algorithms, large-scale problems pose significant challenges to traditional algorithms that are mainly designed to be implemented on a single computing unit. The exploding volume of data (and hence, the problem size), however, may overwhelm any such units. In this paper, we propose a distributed algorithm for general, non-separable, large-scale convex QCQPs, using a novel idea of predictor-corrector primal-dual update with an adaptive step size. The algorithm enables distributed storage of data as well as parallel distributed computing. We establish the conditions for the proposed algorithm to converge to a global optimum, and implement our algorithm on a computer cluster with multiple nodes using Message Passing Interface (MPI). The numerical experiments are conducted on data sets of various scales from different applications, and the results show that our algorithm exhibits favorable scalability for solving large-scale problems.