On the Tightness of the Lagrangian Dual Bound for Alternating Current Optimal Power Flow

Abstract

We study tightness and scalability properties of a Lagrangian dual (LD) bound for the nonconvex alternating current optimal power flow (ACOPF) problem. We show that the LD bound is as tight as that provided by the powerful and popular semidefinite programming relaxation. However, a key advantage of the proposed bound is that it can be computed in a parallel, decentralized manner. Specifically, in the proposed approach we partition the network into a set of subnetworks, we dualize the coupling constraints (giving the LD function), and we maximize the LD function with respect to the dual variables of the coupling constraints (giving the desired LD bound). The dual variables that maximize the LD are obtained by using a bundle method and we provide a proof of convergence for such method. We demonstrate our developments using PGLib test instances.

Leveraging GPU batching for scalable nonlinear programming through massive Lagrangian decomposition

“…Our batch nonlinear programming solver is extremely important in the new optimization algorithm paradigm that solves a large-scale optimization by various decomposition methods (e.g., [34,44,40]). In particular, our solver enables the scalable solution of large-scale nonlinear constrained optimization problem solely on GPUs.…”