neADMM: Nonconvex generalization of Alternating Direction Method of Multipliers for nonlinear equality constrained problems

This is the implmentation of the nonlinear-equality Alternating Direction Method of Multipliers (neADMM).

How to Use

The codes of this paper are in two folders:

1. Numerical examples folder contains two source files example1.m and example2.m.

2. Application folder contains source codes for two applications:

   (i). For 1-bit compressive sensing, run the file main.m.

   (ii). For vaccine adverse event detection, run the file main.m.

Cite

@article{WANG2021100009,

title = {Nonconvex generalization of Alternating Direction Method of Multipliers for nonlinear equality constrained problems},

journal = {Results in Control and Optimization},

pages = {100009},

year = {2021},

issn = {2666-7207},

doi = {https://doi.org/10.1016/j.rico.2021.100009 },

url = { https://www.sciencedirect.com/science/article/pii/S2666720721000035 },

author = {Junxiang Wang and Liang Zhao},

keywords = {Nonconvex ADMM, Nonlinear equality constraints, Spherical constraints, Multi-instance learning},

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.} }