Fast and Stable Nonconvex Constrained Distributed Optimization: The ELLADA Algorithm

TL;DR

The paper introduces ELLADA, a novel distributed optimization algorithm that combines multiple modifications to ADMM, achieving global convergence, efficiency, and stability for nonconvex constrained problems, with applications in distributed nonlinear MPC.

Contribution

It proposes ELLADA, a new distributed optimization method that integrates an extra-layer architecture, approximate NLP solving, and Anderson acceleration for improved convergence and stability.

Findings

Theoretical convergence to stationary solutions is established.

ELLADA reduces iteration count via modified Anderson acceleration.

Demonstrated effectiveness in a distributed nonlinear MPC benchmark.

Abstract

Distributed optimization, where the computations are performed in a localized and coordinated manner using multiple agents, is a promising approach for solving large-scale optimization problems, e.g., those arising in model predictive control (MPC) of large-scale plants. However, a distributed optimization algorithm that is computationally efficient, globally convergent, amenable to nonconvex constraints and general inter-subsystem interactions remains an open problem. In this paper, we combine three important modifications to the classical alternating direction method of multipliers (ADMM) for distributed optimization. Specifically, (i) an extra-layer architecture is adopted to accommodate nonconvexity and handle inequality constraints, (ii) equality-constrained nonlinear programming (NLP) problems are allowed to be solved approximately, and (iii) a modified Anderson acceleration is employed for reducing the number of iterations. Theoretical convergence towards stationary solutions and computational complexity of the proposed algorithm, named ELLADA, is established. Its application to distributed nonlinear MPC is also described and illustrated through a benchmark process system.