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-<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · DividedRectangles.jl</title><meta name="title" content="Home · DividedRectangles.jl"/><meta property="og:title" content="Home · DividedRectangles.jl"/><meta property="twitter:title" content="Home · DividedRectangles.jl"/><meta name="description" content="Documentation for DividedRectangles.jl."/><meta property="og:description" content="Documentation for DividedRectangles.jl."/><meta property="twitter:description" content="Documentation for DividedRectangles.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script data-outdated-warner src="assets/warner.js"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 href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" 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class="tocitem" href>Home</a></li><li><a class="tocitem" href="installation/">Installation</a></li><li><a class="tocitem" href="usage/">Usage</a></li><li><a class="tocitem" href="theory/">Theory</a></li><li><a class="tocitem" href="algorithm/">Algorithm</a></li><li><a class="tocitem" href="credits/">Credits</a></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>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/sisl/DividedRectangles.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/sisl/DividedRectangles.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="DividedRectangles.jl"><a class="docs-heading-anchor" href="#DividedRectangles.jl">DividedRectangles.jl</a><a id="DividedRectangles.jl-1"></a><a class="docs-heading-anchor-permalink" href="#DividedRectangles.jl" title="Permalink"></a></h1><p><a href="https://github.com/sisl/DividedRectangles.jl/actions/workflows/CI.yml"><img src="https://github.com/sisl/DividedRectangles.jl/actions/workflows/CI.yml/badge.svg" alt="CI"/></a> <a href="https://sisl.github.io/DividedRectangles.jl/"><img src="https://img.shields.io/badge/docs-latest-blue.svg" alt="Documentation Status"/></a> <a href="https://codecov.io/gh/sisl/DividedRectangles.jl"><img src="https://codecov.io/gh/sisl/DividedRectangles.jl/graph/badge.svg?token=YALXFAP7UO" alt="codecov"/></a> –-</p><p><strong>DividedRectangles.jl</strong> provides an implementation of the DIRECT (DIvided RECTangles) algorithm for global optimization. The DIRECT algorithm is particularly useful for optimizing functions where the Lipschitz constant is unknown. This package allows users to perform both univariate and multivariate optimization efficiently.</p><h3 id="Key-Equation:"><a class="docs-heading-anchor" href="#Key-Equation:">Key Equation:</a><a id="Key-Equation:-1"></a><a class="docs-heading-anchor-permalink" href="#Key-Equation:" title="Permalink"></a></h3><p>The algorithm is guided by the following fundamental equation:</p><p class="math-container">\[f(x) = \sum_{i=1}^{n} c_i x_i\]</p><p>where:</p><ul><li>(<span>$x_i$</span>) represents the variables.</li><li>(<span>$c_i$</span>) represents the coefficients corresponding to each variable.</li></ul><p>This equation forms the basis for dividing the search space into smaller rectangles, optimizing the function by evaluating it at specific points.</p><hr/><p>This documentation provides detailed usage examples, theoretical background, and advanced customization options to help you get the most out of <code>DividedRectangles.jl</code>.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="installation/">Installation »</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 1.7.0 on <span class="colophon-date" title="Saturday 14 September 2024 17:42">Saturday 14 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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class="docs-right"><a class="docs-navbar-link" href="https://github.com/sisl/DividedRectangles.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/sisl/DividedRectangles.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="DividedRectangles.jl"><a class="docs-heading-anchor" href="#DividedRectangles.jl">DividedRectangles.jl</a><a id="DividedRectangles.jl-1"></a><a class="docs-heading-anchor-permalink" href="#DividedRectangles.jl" title="Permalink"></a></h1><p><a href="https://github.com/sisl/DividedRectangles.jl/actions/workflows/CI.yml"><img src="https://github.com/sisl/DividedRectangles.jl/actions/workflows/CI.yml/badge.svg" alt="CI"/></a> <a href="https://sisl.github.io/DividedRectangles.jl/"><img src="https://img.shields.io/badge/docs-latest-blue.svg" alt="Documentation Status"/></a> <a href="https://codecov.io/gh/sisl/DividedRectangles.jl"><img src="https://codecov.io/gh/sisl/DividedRectangles.jl/graph/badge.svg?token=YALXFAP7UO" alt="codecov"/></a> –-</p><p><strong>DividedRectangles.jl</strong> provides an implementation of the DIRECT (DIvided RECTangles) algorithm for global optimization. The DIRECT algorithm is particularly useful for optimizing functions where the Lipschitz constant is unknown. This package allows users to perform both univariate and multivariate optimization efficiently.</p><h3 id="Key-Equation:"><a class="docs-heading-anchor" href="#Key-Equation:">Key Equation:</a><a id="Key-Equation:-1"></a><a class="docs-heading-anchor-permalink" href="#Key-Equation:" title="Permalink"></a></h3><p>The algorithm is guided by the following fundamental equation:</p><p class="math-container">\[f(x) = \sum_{i=1}^{n} c_i x_i\]</p><p>where:</p><ul><li>(<span>$x_i$</span>) represents the variables.</li><li>(<span>$c_i$</span>) represents the coefficients corresponding to each variable.</li></ul><p>This equation forms the basis for dividing the search space into smaller rectangles, optimizing the function by evaluating it at specific points.</p><hr/><p>This documentation provides detailed usage examples, theoretical background, and advanced customization options to help you get the most out of <code>DividedRectangles.jl</code>.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="installation/">Installation »</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 1.7.0 on <span class="colophon-date" title="Saturday 14 September 2024 17:43">Saturday 14 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>