# Linearization of ReLU Activation Function for Neural Network-Embedded Optimization: Optimal Day-Ahead Energy Scheduling

arXiv: https://arxiv.org/abs/2310.01758 · HTML: https://mlsanity.com/paper/2310.01758/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 3 Oct 2023.

## Builds on (most cited first, 12 of 12)

- [A Review of Graph Neural Networks and Their Applications in Power Systems](https://mlsanity.com/paper/2101.10025/) (2021)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [Learning ReLU Networks on Linearly Separable Data: Algorithm, Optimality, and Generalization](https://mlsanity.com/paper/1808.04685/) (2018)
- [Power Flow Balancing with Decentralized Graph Neural Networks](https://mlsanity.com/paper/2111.02169/) (2021)
- [Reduced Optimal Power Flow Using Graph Neural Network](https://mlsanity.com/paper/2206.13591/) (2022)
- [Singular Values for ReLU Layers](https://mlsanity.com/paper/1812.02566/) (2018)
- [Wholesale Electricity Price Forecasting using Integrated Long-term Recurrent Convolutional Network Model](https://mlsanity.com/paper/2112.13681/) (2021)
- [Security-Constrained Unit Commitment Con-sidering Locational Frequency Stability in Low-Inertia Power Grids](https://mlsanity.com/paper/2110.11498/) (2021)
- [Microgrid Optimal Energy Scheduling Considering Neural Network based Battery Degradation](https://mlsanity.com/paper/2202.12416/) (2022)
- [An Alternative Method for Solving Security-Constrained Unit Commitment with Neural Network Based Battery Degradation Model](https://mlsanity.com/paper/2207.00650/) (2022)
- [A Novel Real-Time Energy Management Strategy for Grid-Supporting Microgrid: Enabling Flexible Trading Power](https://mlsanity.com/paper/2104.14635/) (2021)
- [Quality Analysis of Battery Degradation Models with Real Battery Aging Experiment Data](https://mlsanity.com/paper/2211.12481/) (2022)

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

- [Efficient reformulations of ReLU deep neural networks for surrogate modelling in power system optimisation](https://mlsanity.com/paper/2601.14673/) (2026)

## Abstract (arXiv)

Recently, neural networks have been widely applied in the power system area. They can be used for better predicting input information and modeling system performance with increased accuracy. In some applications such as battery degradation neural network-based microgrid day-ahead energy scheduling, the input features of the trained learning model are variables to be solved in optimization models that enforce limits on the output of the same learning model. This will create a neural network-embedded optimization problem; the use of nonlinear activation functions in the neural network will make such problems extremely hard to solve if not unsolvable. To address this emerging challenge, this paper investigated different methods for linearizing the nonlinear activation functions with a particular focus on the widely used rectified linear unit (ReLU) function. Four linearization methods tailored for the ReLU activation function are developed, analyzed and compared in this paper. Each method employs a set of linear constraints to replace the ReLU function, effectively linearizing the optimization problem, which can overcome the computational challenges associated with the nonlinearity of the neural network model. These proposed linearization methods provide valuable tools for effectively solving optimization problems that integrate neural network models with ReLU activation functions