# KKT-based optimality conditions for neural network approximation

arXiv: https://arxiv.org/abs/2506.17305 · HTML: https://mlsanity.com/paper/2506.17305/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2025.

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

- [LEAF: A Learning-Enabled ADMM Framework for Accelerated Convex Optimization](https://mlsanity.com/paper/2606.08993/) (2026)

## Abstract (arXiv)

In this paper, we obtain necessary optimality conditions for neural network approximation. We consider neural networks in Manhattan (l1 norm) and Chebyshev (max norm). The optimality conditions are based on neural networks with at most one hidden layer. We reformulate nonsmooth unconstrained optimisation problems as larger dimension constrained problems with smooth objective functions and constraints. Then we use KKT conditions to develop the necessary conditions and present the optimality conditions in terms of convex analysis and convex sets.