-<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Introduction · PlasmoAlgorithms.jl</title><meta name="title" content="Introduction · PlasmoAlgorithms.jl"/><meta property="og:title" content="Introduction · PlasmoAlgorithms.jl"/><meta property="twitter:title" content="Introduction · PlasmoAlgorithms.jl"/><meta name="description" content="Documentation for PlasmoAlgorithms.jl."/><meta property="og:description" content="Documentation for PlasmoAlgorithms.jl."/><meta property="twitter:description" content="Documentation for PlasmoAlgorithms.jl."/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link 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id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Introduction</a></li><li><span class="tocitem">PlasmoBenders.jl</span><ul><li><a class="tocitem" href="PlasmoBenders/introduction/">Introduction</a></li><li><a class="tocitem" href="PlasmoBenders/algorithm/">Algorithm</a></li><li><a class="tocitem" href="PlasmoBenders/quickstart/">Quickstart</a></li><li><a class="tocitem" href="PlasmoBenders/solver/">Solver Options</a></li><li><a class="tocitem" href="PlasmoBenders/graph_structure/">Exploiting Graph Structure</a></li><li><a class="tocitem" href="PlasmoBenders/api_docs/">API Documentation</a></li><li><input class="collapse-toggle" id="menuitem-2-7" type="checkbox"/><label class="tocitem" for="menuitem-2-7"><span class="docs-label">Tutorials</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="PlasmoBenders/storage_tutorial/">Storage Operation</a></li><li><a class="tocitem" href="PlasmoBenders/sizing_tutorial/">Equipment Sizing</a></li></ul></li></ul></li><li><span class="tocitem">PlasmoSchwarz.jl</span><ul><li><a class="tocitem" href="PlasmoSchwarz/introduction/">Introduction</a></li><li><a class="tocitem" href="PlasmoSchwarz/quickstart/">Quickstart</a></li><li><a class="tocitem" href="PlasmoSchwarz/algorithm/">Algorithm</a></li><li><a class="tocitem" href="PlasmoSchwarz/api_docs/">API Documentation</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Introduction</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Introduction</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/plasmo-dev/PlasmoAlgorithms.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/plasmo-dev/PlasmoAlgorithms.jl/blob/main/docs/src/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="PlasmoAlgorithms.jl"><a class="docs-heading-anchor" href="#PlasmoAlgorithms.jl">PlasmoAlgorithms.jl</a><a id="PlasmoAlgorithms.jl-1"></a><a class="docs-heading-anchor-permalink" href="#PlasmoAlgorithms.jl" title="Permalink"></a></h1><p>PlasmoAlgorithms is a library of decomposition approaches in <a href="https://julialang.org">Julia</a> that have been implemented for <a href="https://github.com/plasmo-dev/Plasmo.jl">Plasmo.jl</a> data structures. Plasmo is an open-source modeling package that constructs graph-structured optimization models. Plasmo is built on an abstraction called an <code>OptiGraph</code>, containing <code>OptiNodes</code> (with objectives, variables, and constraints) and <code>OptiEdges</code> (with constraints for variables on two or more nodes). </p><p>PlasmoAlgorithms is intended to include different decomposition approaches that can exploit the graph structure of an optimization, and the implementation of these algorithms is based upon the graph structure. Currently, the following are implemented in this repository: </p><ul><li><a href="https://en.wikipedia.org/wiki/Benders_decomposition">Benders Decomposition</a> is implemented through the package PlasmoBenders.jl that is contained in this repository. PlasmoBenders.jl applies Benders and Nested Benders Decompositions to a problem defined by the user in Plasmo. PlasmoBenders applies these decomposition approaches based on the structure defined by the graph, where the graph structure dictates the complicating variables for the algorithm. Benders can be used for LP and MILP problems.</li><li><a href="https://arxiv.org/abs/1810.00491">Overlapping Schwarz Decomposition</a> is implemented throught he package PlasmoSchwarz.jl (formerly <a href="https://github.com/plasmo-dev/SchwarzOpt.jl">SchwarzOpt.jl</a>). PlasmoSchwarz.jl uses a partitioned graph and overlaps the partitioned regions with their neighboring partitions. Each overlapped subgraph is optimized and information is then shared between the subgraphs. Overlapping Schwarz can be used for NLP problems. </li></ul><p>Other decomposition approaches could likewise be developed. We welcome contributions to the PlasmoAlgorithms suite. In addition, we encourage reporting issues and feature requests via the <a href="https://github.com/plasmo-dev/PlasmoAlgorithms.jl/issues">GitHub issue tracker.</a>.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="PlasmoBenders/introduction/">Introduction »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.15.0 on <span class="colophon-date" title="Thursday 6 November 2025 16:10">Thursday 6 November 2025</span>. 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