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auburn-comp-math · Feb 15, 2024 · f24ad3c · f24ad3c
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diff --git a/Intro.html b/Intro.html
@@ -424,7 +424,7 @@ <h2>Formulation of Optimization Problems<a class="headerlink" href="#formulation
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-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7f5a1012afa0&gt;
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7fd2282e1fa0&gt;
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@@ -504,7 +504,7 @@ <h3>Fundamentals of unconstrained optimization<a class="headerlink" href="#funda
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-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.collections.PathCollection at 0x7f59fc488df0&gt;
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.collections.PathCollection at 0x7fd229447d90&gt;
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@@ -531,7 +531,7 @@ <h3>Fundamentals of unconstrained optimization<a class="headerlink" href="#funda
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-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7f59ee6d4550&gt;
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7fd214694550&gt;
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diff --git a/LineSearch.html b/LineSearch.html
@@ -340,6 +340,7 @@ <h2> Contents </h2>
             </div>
             <nav aria-label="Page">
                 <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#descent-direction">Descent Direction</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#step-length">Step Length</a><ul class="nav section-nav flex-column">
 <li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#wolfe-conditions">Wolfe Conditions</a></li>
 <li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#goldstein-conditions">Goldstein Conditions</a></li>
@@ -372,6 +373,9 @@ <h2> Contents </h2>
 
   <section class="tex2jax_ignore mathjax_ignore" id="line-search-methods">
 <h1>Line Search Methods<a class="headerlink" href="#line-search-methods" title="Link to this heading">#</a></h1>
+<section id="descent-direction">
+<h2>Descent Direction<a class="headerlink" href="#descent-direction" title="Link to this heading">#</a></h2>
+</section>
 <section id="step-length">
 <h2>Step Length<a class="headerlink" href="#step-length" title="Link to this heading">#</a></h2>
 <p>Each iteration of line search methods requires a step length <span class="math notranslate nohighlight">\(\alpha_k\)</span> and a search direction <span class="math notranslate nohighlight">\(p_k\)</span> to be computed, the update is</p>
@@ -568,6 +572,7 @@ <h3>Programming<a class="headerlink" href="#programming" title="Link to this hea
   </div>
   <nav class="bd-toc-nav page-toc">
     <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#descent-direction">Descent Direction</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#step-length">Step Length</a><ul class="nav section-nav flex-column">
 <li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#wolfe-conditions">Wolfe Conditions</a></li>
 <li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#goldstein-conditions">Goldstein Conditions</a></li>

diff --git a/_sources/LineSearch.md b/_sources/LineSearch.md
@@ -12,6 +12,8 @@ kernelspec:
 
 # Line Search Methods
 
+## Descent Direction
+
 ## Step Length
 
 Each iteration of line search methods requires a step length $\alpha_k$ and a search direction $p_k$ to be computed, the update is