A Julia Framework for Graph-Structured Nonlinear Optimization
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866917472465059840 |
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| author | Cole, David L Shin, Sungho Zavala, Victor |
| author_facet | Cole, David L Shin, Sungho Zavala, Victor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_05264 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Julia Framework for Graph-Structured Nonlinear Optimization Cole, David L Shin, Sungho Zavala, Victor Optimization and Control 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. |
| title | A Julia Framework for Graph-Structured Nonlinear Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2204.05264 |