# MADMM: a generic algorithm for non-smooth optimization on manifolds

arXiv: https://arxiv.org/abs/1505.07676 · HTML: https://mlsanity.com/paper/1505.07676/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2015.

## Built on by (most cited first, 12 of 12)

- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [Causal Abstraction Learning based on the Semantic Embedding Principle](https://mlsanity.com/paper/2502.00407/) (2025)
- [Non-Isometric Shape Matching via Functional Maps on Landmark-Adapted Bases](https://mlsanity.com/paper/2205.04800/) (2022)
- [Learning Graphical Factor Models with Riemannian Optimization](https://mlsanity.com/paper/2210.11950/) (2022)
- [A Riemannian ADMM](https://mlsanity.com/paper/2211.02163/) (2022)
- [Learning Canonical Embeddings for Unsupervised Shape Correspondence with Locally Linear Transformations](https://mlsanity.com/paper/2209.02152/) (2022)
- [Finite-Time Analysis of Stochastic Nonconvex Nonsmooth Optimization on the Riemannian Manifolds](https://mlsanity.com/paper/2510.21468/) (2025)
- [Sparse Partial Least Squares for Coarse Noisy Graph Alignment](https://mlsanity.com/paper/2104.02810/) (2021)
- [A Riemannian smoothing steepest descent method for non-Lipschitz optimization on submanifolds](https://mlsanity.com/paper/2104.04199/) (2021)
- [Learning Graph Filters for Structure-Function Coupling based Hub Node Identification](https://mlsanity.com/paper/2410.17410/) (2024)
- [Leveraging Low-rank Factorizations of Conditional Correlation Matrices in Graph Learning](https://mlsanity.com/paper/2506.10628/) (2025)
- [Primal-Dual Methods for Nonsmooth Nonconvex Optimization with Orthogonality Constraints](https://mlsanity.com/paper/2604.04130/) (2026)

## Abstract (arXiv)

Numerous problems in machine learning are formulated as optimization with manifold constraints. In this paper, we propose the Manifold alternating directions method of multipliers (MADMM), an extension of the classical ADMM scheme for manifold-constrained non-smooth optimization problems and show its application to several challenging problems in dimensionality reduction, data analysis, and manifold learning.