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julia> highs_knapsack([1.0, 2.0], [0.5, 0.5], 1.25)
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2.0</code></pre><p>We&#39;ve now gone from a algebraic model that looked identical to the mathematical model we started with, to a verbose function that uses HiGHS-specific functionality.</p><p>The difference between <code>algebraic_knapsack</code> and <code>highs_knapsack</code> highlights the benefit that algebraic modeling languages provide to users. Moreover, if we used a different solver, the solver-specific function would be entirely different. A key benefit of an algebraic modeling language is that you can change the solver without needing to rewrite the model.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../api/JuMP.Containers/">« JuMP.Containers</a><a class="docs-footer-nextpage" href="../bibliography/">Bibliography »</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 1.16.1 on <span class="colophon-date" title="Thursday 26 February 2026 01:26">Thursday 26 February 2026</span>. Using Julia version 1.12.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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2.0</code></pre><p>We&#39;ve now gone from a algebraic model that looked identical to the mathematical model we started with, to a verbose function that uses HiGHS-specific functionality.</p><p>The difference between <code>algebraic_knapsack</code> and <code>highs_knapsack</code> highlights the benefit that algebraic modeling languages provide to users. Moreover, if we used a different solver, the solver-specific function would be entirely different. A key benefit of an algebraic modeling language is that you can change the solver without needing to rewrite the model.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../api/JuMP.Containers/">« JuMP.Containers</a><a class="docs-footer-nextpage" href="../bibliography/">Bibliography »</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 1.16.1 on <span class="colophon-date" title="Sunday 1 March 2026 21:50">Sunday 1 March 2026</span>. Using Julia version 1.12.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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- [ ] Implement `vectorize(data, ::NewShape)::Vector`
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- [ ] Add the tests from https://github.com/jump-dev/JuMP.jl/pull/3816</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../roadmap/">« Roadmap</a><a class="docs-footer-nextpage" href="../../packages/solvers/">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 1.16.1 on <span class="colophon-date" title="Thursday 26 February 2026 01:26">Thursday 26 February 2026</span>. Using Julia version 1.12.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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- [ ] Add the tests from https://github.com/jump-dev/JuMP.jl/pull/3816</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../roadmap/">« Roadmap</a><a class="docs-footer-nextpage" href="../../packages/solvers/">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 1.16.1 on <span class="colophon-date" title="Sunday 1 March 2026 21:50">Sunday 1 March 2026</span>. Using Julia version 1.12.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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$ git pull</code></pre><div class="admonition is-info" id="Note-cbfb439166b2b2cd"><header class="admonition-header">Note<a class="admonition-anchor" href="#Note-cbfb439166b2b2cd" title="Permalink"></a></header><div class="admonition-body"><p>If you have suggestions to improve this guide, please make a pull request. It&#39;s particularly helpful if you do this after your first pull request because you&#39;ll know all the parts that could be explained better.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../background/bibliography/">« Bibliography</a><a class="docs-footer-nextpage" href="../extensions/">Extensions »</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 1.16.1 on <span class="colophon-date" title="Thursday 26 February 2026 01:26">Thursday 26 February 2026</span>. Using Julia version 1.12.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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$ git pull</code></pre><div class="admonition is-info" id="Note-cbfb439166b2b2cd"><header class="admonition-header">Note<a class="admonition-anchor" href="#Note-cbfb439166b2b2cd" title="Permalink"></a></header><div class="admonition-body"><p>If you have suggestions to improve this guide, please make a pull request. It&#39;s particularly helpful if you do this after your first pull request because you&#39;ll know all the parts that could be explained better.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../background/bibliography/">« Bibliography</a><a class="docs-footer-nextpage" href="../extensions/">Extensions »</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 1.16.1 on <span class="colophon-date" title="Sunday 1 March 2026 21:50">Sunday 1 March 2026</span>. Using Julia version 1.12.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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1.0</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; set_attribute(c, MOI.ConstraintDualStart(), [2.0, -1.0, 1.0])</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; dual_start_value(c)</code><code class="nohighlight hljs ansi" style="display:block;">2×2 LinearAlgebra.Symmetric{Float64, Matrix{Float64}}:
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-1.0 1.0</code></pre><h2 id="unset_-methods"><a class="docs-heading-anchor" href="#unset_-methods"><code>unset_</code> methods</a><a id="unset_-methods-1"></a><a class="docs-heading-anchor-permalink" href="#unset_-methods" title="Permalink"></a></h2><p>There are a variety of attributes in JuMP and MOI that can be &quot;set&quot; and &quot;unset.&quot; For example, there is <a href="../../moi/reference/models/#MathOptInterface.Silent"><code>MOI.Silent</code></a>, and the corresponding <a href="../../api/JuMP/#set_silent"><code>set_silent</code></a> and <a href="../../api/JuMP/#unset_silent"><code>unset_silent</code></a>.</p><p>Note how <a href="../../api/JuMP/#set_silent"><code>set_silent</code></a> and <a href="../../api/JuMP/#unset_silent"><code>unset_silent</code></a> take a single argument (the model), where <code>set_silent(model)</code> corresponds to <code>MOI.set(model, MOI.Silent(), true)</code> and <code>unset_silent(model)</code> corresponds to <code>MOI.set(model, MOI.Silent(), false)</code>. We could have instead implemented a single method <code>set_silent(model, flag::Bool)</code> that corresponded to <code>MOI.set(model, MOI.Silent(), flag)</code>. Another example is <a href="../../api/JuMP/#unset_time_limit_sec"><code>unset_time_limit_sec</code></a>, which is equivalent to <code>set_time_limit_sec(model, nothing)</code>.</p><p>We have come to regard the <code>unset_</code> design as a mistake, because it leads to a proliferation of unique function names instead of leveraging Julia&#39;s strength for multiple dispatch.</p><p>The existing <code>unset_</code> names are retained for backwards compatibility, but, going forward, provide a single <code>set_</code> method and document what value type should be provided to restore the model to the default setting. Thus, we have <a href="../../api/JuMP/#set_string_names_on_creation"><code>set_string_names_on_creation</code></a>, but no corresponding <code>unset_string_names_on_creation</code>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../style/">« Style Guide</a><a class="docs-footer-nextpage" href="../roadmap/">Roadmap »</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 1.16.1 on <span class="colophon-date" title="Thursday 26 February 2026 01:26">Thursday 26 February 2026</span>. Using Julia version 1.12.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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-1.0 1.0</code></pre><h2 id="unset_-methods"><a class="docs-heading-anchor" href="#unset_-methods"><code>unset_</code> methods</a><a id="unset_-methods-1"></a><a class="docs-heading-anchor-permalink" href="#unset_-methods" title="Permalink"></a></h2><p>There are a variety of attributes in JuMP and MOI that can be &quot;set&quot; and &quot;unset.&quot; For example, there is <a href="../../moi/reference/models/#MathOptInterface.Silent"><code>MOI.Silent</code></a>, and the corresponding <a href="../../api/JuMP/#set_silent"><code>set_silent</code></a> and <a href="../../api/JuMP/#unset_silent"><code>unset_silent</code></a>.</p><p>Note how <a href="../../api/JuMP/#set_silent"><code>set_silent</code></a> and <a href="../../api/JuMP/#unset_silent"><code>unset_silent</code></a> take a single argument (the model), where <code>set_silent(model)</code> corresponds to <code>MOI.set(model, MOI.Silent(), true)</code> and <code>unset_silent(model)</code> corresponds to <code>MOI.set(model, MOI.Silent(), false)</code>. We could have instead implemented a single method <code>set_silent(model, flag::Bool)</code> that corresponded to <code>MOI.set(model, MOI.Silent(), flag)</code>. Another example is <a href="../../api/JuMP/#unset_time_limit_sec"><code>unset_time_limit_sec</code></a>, which is equivalent to <code>set_time_limit_sec(model, nothing)</code>.</p><p>We have come to regard the <code>unset_</code> design as a mistake, because it leads to a proliferation of unique function names instead of leveraging Julia&#39;s strength for multiple dispatch.</p><p>The existing <code>unset_</code> names are retained for backwards compatibility, but, going forward, provide a single <code>set_</code> method and document what value type should be provided to restore the model to the default setting. Thus, we have <a href="../../api/JuMP/#set_string_names_on_creation"><code>set_string_names_on_creation</code></a>, but no corresponding <code>unset_string_names_on_creation</code>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../style/">« Style Guide</a><a class="docs-footer-nextpage" href="../roadmap/">Roadmap »</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 1.16.1 on <span class="colophon-date" title="Sunday 1 March 2026 21:49">Sunday 1 March 2026</span>. Using Julia version 1.12.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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