# Neural Optimization Machine: A Neural Network Approach for Optimization

arXiv: https://arxiv.org/abs/2208.03897 · HTML: https://mlsanity.com/paper/2208.03897/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 59 references that are in the map.
- First posted on arXiv 8 Aug 2022.

## Builds on (most cited first, 2 of 2)

- [Predicting atmospheric optical properties for radiative transfer computations using neural networks](https://mlsanity.com/paper/2005.02265/) (2020)
- [Neuro-Optimization: Learning Objective Functions Using Neural Networks](https://mlsanity.com/paper/1905.10079/) (2019)

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

- [Physics-Driven ML-Based Modelling for Correcting Inverse Estimation](https://mlsanity.com/paper/2309.13985/) (2023)
- [Into the Void: Mapping the Unseen Gaps in High Dimensional Data](https://mlsanity.com/paper/2501.15273/) (2025)
- [A Guaranteed-Stable Neural Network Approach for Optimal Control of Nonlinear Systems](https://mlsanity.com/paper/2501.17333/) (2025)
- [Covariance-Aware Transformers for Quadratic Programming and Decision Making](https://mlsanity.com/paper/2602.14506/) (2026)

## Abstract (arXiv)

A novel neural network (NN) approach is proposed for constrained optimization. The proposed method uses a specially designed NN architecture and training/optimization procedure called Neural Optimization Machine (NOM). The objective functions for the NOM are approximated with NN models. The optimization process is conducted by the neural network's built-in backpropagation algorithm. The NOM solves optimization problems by extending the architecture of the NN objective function model. This is achieved by appropriately designing the NOM's structure, activation function, and loss function. The NN objective function can have arbitrary architectures and activation functions. The application of the NOM is not limited to specific optimization problems, e.g., linear and quadratic programming. It is shown that the increase of dimension of design variables does not increase the computational cost significantly. Then, the NOM is extended for multiobjective optimization. Finally, the NOM is tested using numerical optimization problems and applied for the optimal design of processing parameters in additive manufacturing.