# Graph-Based Modeling and Decomposition of Energy Infrastructures

arXiv: https://arxiv.org/abs/2010.02404 · HTML: https://mlsanity.com/paper/2010.02404/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2020.

## Built on by (most cited first, 2 of 2)

- [Accelerating process control and optimization via machine learning: A review](https://mlsanity.com/paper/2412.18529/) (2024)
- [Learning-enabled Acceleration of Scenario-based Model Predictive Control](https://mlsanity.com/paper/2607.12775/) (2026)

## Abstract (arXiv)

Nonlinear optimization problems are found at the heart of real-time operations of critical infrastructures. These problems are computationally challenging because they embed complex physical models that exhibit space-time dynamics. We propose modeling these problems as graph-structured optimization problems, and illustrate how their structure can be exploited at the modeling level (for parallelizing function/derivative computations) and at the solver level (for parallelizing linear algebra operations). Specifically, we present a restricted additive Schwarz scheme that enables flexible decomposition of complex graph structures within an interior-point algorithm. The proposed approach is implemented as a general-purpose nonlinear programming solver that we call MadNLP.jl; this Julia-based solver is interfaced to the graph-based modeling package Plasmo.jl. The efficiency of this framework is demonstrated via problems arising in transient gas network optimization and multi-period AC optimal power flow. We show that our framework accelerates the solution (compared to off-the-shelf tools) by over 300%; specifically, solution times are reduced from 72.36 sec to 23.84 sec for the gas problem and from 515.81 sec to 149.45 sec for the power flow problem.