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DOI: 10.23952/cot.2027.17
Received December 12, 2025; Accepted March 31, 2026; Published online October 23, 2026
Abstract. In this paper, we obtain necessary optimality conditions for neural network approximation. We consider neural networks in Manhattan (
norm) and Chebyshev (max norm). The activation functions are restricted to the class of smooth functions. 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.
How to Cite this Article:
V. Peiris, N. Sukhorukova, J. Ugon, KKT-based optimality conditions for neural network approximation, Commun. Optim. Theory 2027 (2027) 17.