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Title: A Julia Framework for Graph-Structured Nonlinear Optimization

Journal Article · · Industrial and Engineering Chemistry Research

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 Julia framework for modeling and solving graph-structured nonlinear optimization problems. Our framework integrates the modeling package Plasmo.jl (which facilitates the construction and manipulation of graph models) and the nonlinear optimization solver 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 Plasmo.jl and how the model structure can be exploited by 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.

Research Organization:
Argonne National Laboratory (ANL), Argonne, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
Journal Information:
Industrial and Engineering Chemistry Research, Vol. 61, Issue 26
Country of Publication:
United States

References (32)

Exponential Decay of Sensitivity in Graph-Structured Nonlinear Programs preprint January 2021
A structure-conveying modelling language for mathematical and stochastic programming journal November 2009
Exploiting structure in parallel implementation of interior point methods for optimization journal December 2008
Parallel interior-point solver for structured linear programs journal June 2003
Parallel cyclic reduction decomposition for dynamic optimization problems journal January 2019
A Nested Schur decomposition approach for multiperiod optimization of chemical processes journal December 2021
Interior-point decomposition approaches for parallel solution of large-scale nonlinear parameter estimation problems journal October 2008
DeCODe: a community-based algorithm for generating high-quality decompositions of optimization problems journal June 2019
Decomposition of control and optimization problems by network structure: Concepts, methods, and inspirations from biology journal July 2019
Graph-based modeling and simulation of complex systems journal June 2019
Decomposition of integrated scheduling and dynamic optimization problems using community detection journal June 2020
Efficient Solution of Enterprise-Wide Optimization Problems Using Nested Stochastic Blockmodeling journal October 2021
Stochastic blockmodeling for learning the structure of optimization problems journal September 2021
Optimal decomposition for distributed optimization in nonlinear model predictive control through community detection journal March 2018
Graph-Based Modeling and Decomposition of Energy Infrastructures journal January 2021
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs journal January 1998
QPSchur: A dual, active-set, Schur-complement method for large-scale and structured convex quadratic programming journal March 2006
An interior-point method for efficient solution of block-structured NLP problems using an implicit Schur-complement decomposition journal December 2014
Application of Interior-Point Methods to Model Predictive Control journal December 1998
Scalable preconditioning of block-structured linear algebra systems using ADMM journal February 2020
Efficient parallel solution of large-scale nonlinear dynamic optimization problems journal April 2014
An Algebraic Convergence Theory for Restricted Additive Schwarz Methods Using Weighted Max Norms journal January 2001
Overlapping Schwarz Decomposition for Constrained Quadratic Programs conference December 2020
Decentralized Schemes With Overlap for Solving Graph-Structured Optimization Problems journal September 2020
Pyomo — Optimization Modeling in Python book January 2017
Pyomo: modeling and solving mathematical programs in Python journal August 2011
Remote Renewable Hubs for Carbon-Neutral Synthetic Fuel Production journal June 2021
PySP: modeling and solving stochastic programs in Python journal March 2012
JuMP: A Modeling Language for Mathematical Optimization journal January 2017
Structured nonconvex optimization of large-scale energy systems using PIPS-NLP conference August 2014
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming journal April 2005
An Optimization-Based State Estimation Framework for Large-Scale Natural Gas Networks journal December 2017