A Julia Framework for Graph-Structured Nonlinear Optimization

Graph theory provides a convenient framework for modeling and solving structured optimization problems. Under this framework, the modeler can arrange/assemble the components of an optimization model (variables, constraints, objective functions, and data) within nodes and edges of a graph, and this r...

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Bibliographic Details
Published in:arXiv.org 2022-04
Main Authors: Cole, David L, Shin, Sungho, Zavala, Victor
Format: Article
Language:English
Subjects:
Constraint modelling
Graph theory
Graphical representations
Optimization
Optimization models
Online Access:Get full text
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Summary:Graph theory provides a convenient framework for modeling and solving structured optimization problems. Under this framework, the modeler can arrange/assemble the components of an optimization model (variables, constraints, objective functions, and data) within nodes and edges of a graph, and this representation can be used to visualize, manipulate, and solve the problem. In this work, we present a \({\tt Julia}\) framework for modeling and solving graph-structured nonlinear optimization problems. Our framework integrates the modeling package \({\tt Plasmo.jl}\) (which facilitates the construction and manipulation of graph models) and the nonlinear optimization solver \({\tt MadNLP.jl}\) (which provides capabilities for exploiting graph structures to accelerate solution). We illustrate with a simple example how model construction and manipulation can be performed in an intuitive manner using \({\tt Plasmo.jl}\) and how the model structure can be exploited by \({\tt MadNLP.jl}\). We also demonstrate the scalability of the framework by targeting a large-scale, stochastic gas network problem that contains over 1.7 million variables.
ISSN:2331-8422