# Constrained composite optimization and augmented Lagrangian methods

arXiv: https://arxiv.org/abs/2203.05276 · HTML: https://mlsanity.com/paper/2203.05276/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2022.

## Built on by (most cited first, 1 of 1)

- [A proximal augmented Lagrangian method for nonconvex optimization with equality and inequality constraints](https://mlsanity.com/paper/2509.02894/) (2025)

## Abstract (arXiv)

We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling framework for a variety of applications. We study stationarity and regularity concepts, and propose a flexible augmented Lagrangian scheme. We provide a theoretical characterization of the algorithm and its asymptotic properties, deriving convergence results for fully nonconvex problems. It is demonstrated how the inner subproblems can be solved by off-the-shelf proximal methods, notwithstanding the possibility to adopt any solvers, insofar as they return approximate stationary points. Finally, we describe our matrix-free implementation of the proposed algorithm and test it numerically. Illustrative examples show the versatility of constrained composite programs as a modeling tool and expose difficulties arising in this vast problem class.