# An Augmented Lagrangian Method for Optimization Problems in Banach Spaces

arXiv: https://arxiv.org/abs/1807.04467 · HTML: https://mlsanity.com/paper/1807.04467/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2018.

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

- [Learning solutions to some toy constrained optimization problems in infinite dimensional Hilbert spaces](https://mlsanity.com/paper/2401.01306/) (2024)

## Abstract (arXiv)

We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of inequality constraints with infinite-dimensional image space. Moreover, we discuss the convergence properties of our algorithm with regard to feasibility, global optimality, and KKT conditions. Some numerical results are given to illustrate the practical viability of the method.