# Smoothed Proximal Lagrangian Method for Nonlinear Constrained Programs

arXiv: https://arxiv.org/abs/2408.15047 · HTML: https://mlsanity.com/paper/2408.15047/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2024.

## Built on by (most cited first, 4 of 4)

- [Single-loop Algorithms for Stochastic Non-convex Optimization with Weakly-Convex Constraints](https://mlsanity.com/paper/2504.15243/) (2025)
- [Inexact Moreau Envelope Lagrangian Method for Non-Convex Constrained Optimization under Local Error Bound Conditions on Constraint Functions](https://mlsanity.com/paper/2502.19764/) (2025)
- [Nonconvex Composite Functional Constraints via First-Order Augmented Lagrangian Methods under Local Regularity](https://mlsanity.com/paper/2607.08954/) (2026)
- [Stochastic Penalty-Barrier Method for Constrained Machine Learning](https://mlsanity.com/paper/2605.18618/) (2026)

## Abstract (arXiv)

This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped, and 2) an first-order iteration complexity of O(ε-2) is established under mild regularity assumptions. The first feature suggests the practical efficiency of the proposed method, while the second feature highlights its theoretical superiority. Numerical experiments on various problem scales demonstrate the advantages of the proposed method in terms of speed and solution quality.