# Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraints

arXiv: https://arxiv.org/abs/2201.07657 · HTML: https://mlsanity.com/paper/2201.07657/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 50 references that are in the map.
- First posted on arXiv 19 Jan 2022.

## Builds on (most cited first, 19 of 19)

- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [Relatively-Smooth Convex Optimization by First-Order Methods, and Applications](https://mlsanity.com/paper/1610.05708/) (2016)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Efficiency of minimizing compositions of convex functions and smooth maps](https://mlsanity.com/paper/1605.00125/) (2016)
- [A globally convergent algorithm for nonconvex optimization based on block coordinate update](https://mlsanity.com/paper/1410.1386/) (2014)
- [Solving (most) of a set of quadratic equalities: Composite optimization for robust phase retrieval](https://mlsanity.com/paper/1705.02356/) (2017)
- [Nonconvex Nonsmooth Low-Rank Minimization via Iteratively Reweighted Nuclear Norm](https://mlsanity.com/paper/1510.06895/) (2015)
- [Algorithms for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence](https://mlsanity.com/paper/2010.01935/) (2020)
- [The proximal alternating direction method of multipliers in the nonconvex setting: convergence analysis and rates](https://mlsanity.com/paper/1801.01994/) (2018)
- [An Inertial Block Majorization Minimization Framework for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2010.12133/) (2020)
- [Linearized ADMM for Non-convex Non-smooth Optimization with Convergence Analysis](https://mlsanity.com/paper/1705.02502/) (2017)
- [Unifying abstract inexact convergence theorems and block coordinate variable metric iPiano](https://mlsanity.com/paper/1602.07283/) (2016)
- [Efficient Algorithms for Large-scale Generalized Eigenvector Computation and Canonical Correlation Analysis](https://mlsanity.com/paper/1604.03930/) (2016)
- [Nonconvex Lagrangian-Based Optimization: Monitoring Schemes and Global Convergence](https://mlsanity.com/paper/1801.03013/) (2018)
- [Iteration-complexity of a Jacobi-type non-Euclidean ADMM for multi-block linearly constrained nonconvex programs](https://mlsanity.com/paper/1705.07229/) (2017)
- [Block Alternating Bregman Majorization Minimization with Extrapolation](https://mlsanity.com/paper/2107.04395/) (2021)
- [A Block Successive Upper Bound Minimization Method of Multipliers for Linearly Constrained Convex Optimization](https://mlsanity.com/paper/1401.7079/) (2014)
- [Extrapolated Proximal Subgradient Algorithms for Nonconvex and Nonsmooth Fractional Programs](https://mlsanity.com/paper/2003.04124/) (2020)
- [A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimization](https://mlsanity.com/paper/2102.05433/) (2021)

## Abstract (arXiv)

This paper proposes a multiblock alternating direction method of multipliers for solving a class of multiblock nonsmooth nonconvex optimization problem with nonlinear coupling constraints. We employ a majorization minimization procedure in the update of each block of the primal variables. Subsequential and global convergence of the generated sequence to a critical point of the augmented Lagrangian are proved. We also establish iteration complexity and provide preliminary numerical results for the proposed algorithm.