Scalable Primal Decomposition Schemes for Large-Scale Infrastructure Networks

TL;DR

This paper introduces primal decomposition schemes for large-scale infrastructure network optimization that ensure high feasibility quickly, outperform ADMM in accuracy, and match the speed of centralized solvers like Ipopt.

Contribution

The paper presents novel primal decomposition methods for hierarchically structured strongly convex QPs that improve feasibility and convergence speed over classical approaches like ADMM.

Findings

Proposed schemes solve large problems as fast as Ipopt.

Schemes require less communication and no full model exchange.

Achieve higher accuracy than ADMM.

Abstract

The operation of large-scale infrastructure networks requires scalable optimization schemes. To guarantee safe system operation, a high degree of feasibility in a small number of iterations is important. Decomposition schemes can help to achieve scalability. In terms of feasibility, however, classical approaches such as the alternating direction method of multipliers (ADMM) often converge slowly. In this work, we present primal decomposition schemes for hierarchically structured strongly convex QPs. These schemes offer high degrees of feasibility in a small number of iterations in combination with global convergence guarantees. We benchmark their performance against the centralized off-the-shelf interior-point solver Ipopt and ADMM on problems with up to 300,000 decision variables and constraints. We find that the proposed approaches solve problems as fast as Ipopt, but with reduced communication and without requiring a full model exchange. Moreover, the proposed schemes achieve a higher accuracy than ADMM.