Decentralized non-convex optimization via bi-level SQP and ADMM

TL;DR

This paper introduces a decentralized bi-level SQP method utilizing ADMM for solving non-convex optimization problems efficiently with convergence guarantees, demonstrated on power flow applications.

Contribution

It proposes a novel bi-level SQP approach with ADMM for inner problems, providing convergence guarantees and improved computational efficiency for decentralized non-convex optimization.

Findings

Method has local convergence guarantees for non-convex problems.

Solves sequences of Quadratic Programs, not Nonlinear Programs.

Shows competitive performance on optimal power flow problems.

Abstract

Decentralized non-convex optimization is important in many problems of practical relevance. Existing decentralized methods, however, typically either lack convergence guarantees for general non-convex problems, or they suffer from a high subproblem complexity. We present a novel bi-level SQP method, where the inner quadratic problems are solved via ADMM. A decentralized stopping criterion from inexact Newton methods allows the early termination of ADMM as an inner algorithm to improve computational efficiency. The method has local convergence guarantees for non-convex problems. Moreover, it only solves sequences of Quadratic Programs, whereas many existing algorithms solve sequences of Nonlinear Programs. The method shows competitive numerical performance for an optimal power flow problem.