Fast and stable nonconvex constrained distributed optimization: the ELLADA algorithm

Abstract

Distributed optimization using multiple computing agents in a localized and coordinated manner 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 remains an open problem. In this paper, we combine three important modifications to the classical alternating direction method of multipliers for distributed optimization. Specifically, (1) an extra-layer architecture is adopted to accommodate nonconvexity and handle inequality constraints, (2) equality-constrained nonlinear programming (NLP) problems are allowed to be solved approximately, and (3) a modified Anderson acceleration is employed for reducing the number of iterations. Theoretical convergence of the proposed algorithm, named ELLADA, is established and its numerical performance is demonstrated on a large-scale NLP benchmark problem. Its application to distributed nonlinear MPC is also described and illustrated through a benchmark process system.