Nonconvex Generalization of Alternating Direction Method of Multipliers for Nonlinear Equality Constrained Problems

TL;DR

This paper extends the ADMM algorithm to handle nonlinear equality constraints, providing globally optimal solutions to nonconvex subproblems, and demonstrates superior performance on synthetic and real datasets.

Contribution

The paper introduces neADMM, a novel extension of ADMM for nonlinear constraints, with methods to solve nonconvex subproblems optimally.

Findings

neADMM outperforms existing methods in experiments

Provides globally optimal solutions for nonconvex subproblems

Demonstrates scalability on real-world datasets

Abstract

The classic Alternating Direction Method of Multipliers (ADMM) is a popular framework to solve linear-equality constrained problems. In this paper, we extend the ADMM naturally to nonlinear equality-constrained problems, called neADMM. The difficulty of neADMM is to solve nonconvex subproblems. We provide globally optimal solutions to them in two important applications. Experiments on synthetic and real-world datasets demonstrate excellent performance and scalability of our proposed neADMM over existing state-of-the-start methods.