论文标题
用于图形结构非线性优化的Julia框架
A Julia Framework for Graph-Structured Nonlinear Optimization
论文作者
论文摘要
图理论为建模和解决结构化优化问题提供了方便的框架。在此框架下，建模者可以在节点和图中安排/组装优化模型（变量，约束，目标函数和数据）的组件，并且该表示形式可用于可视化，操纵和解决问题。在这项工作中，我们提出了一个$ {\ tt Julia} $框架，用于建模和求解图形结构化的非线性优化问题。我们的框架集成了建模软件包$ {\ tt plasmo.jl} $（有助于图形模型的构造和操纵）和非线性优化求解器$ {\ tt madnlp.jl} $（为利用图形结构的功能提供了可加速解决方案的功能）。我们用一个简单的示例说明了如何使用$ {\ tt plasmo.jl} $以直观的方式执行模型构建和操纵，以及如何通过$ {\ tt madnlp.jl} $利用模型结构。我们还通过针对包含超过170万个变量的大规模随机气体网络问题来证明框架的可扩展性。
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.
