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@@ -12635,46 +12635,14 @@ <h4 id="TASK">TASK<a class="anchor-link" href="#TASK">&#182;</a></h4><ol>
 
     <span class="c"># your turn!</span>
     <span class="k">function</span> <span class="n">resid</span><span class="p">(</span><span class="n">c</span><span class="o">::</span><span class="kt">Vector</span><span class="p">,</span><span class="n">result</span><span class="o">::</span><span class="kt">Vector</span><span class="p">,</span><span class="n">p</span><span class="p">,</span><span class="n">basis</span><span class="p">,</span><span class="n">alpha</span><span class="p">,</span><span class="n">eta</span><span class="p">)</span>
-        <span class="n">q</span> <span class="o">=</span> <span class="n">funeval</span><span class="p">(</span><span class="n">c</span><span class="p">,</span><span class="n">basis</span><span class="p">,</span><span class="n">p</span><span class="p">)[</span><span class="mi">1</span><span class="p">]</span>
-        <span class="n">q2</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">(</span><span class="n">q</span><span class="p">)</span>
-        <span class="k">for</span> <span class="n">i</span> <span class="kp">in</span> <span class="n">eachindex</span><span class="p">(</span><span class="n">q2</span><span class="p">)</span>
-            <span class="k">if</span> <span class="n">q</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;</span> <span class="mi">0</span>
-                <span class="n">q2</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mf">20.0</span>
-            <span class="k">else</span>
-                <span class="n">q2</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">q</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
-            <span class="k">end</span>
-        <span class="k">end</span>
-        <span class="n">result</span><span class="p">[</span><span class="o">:</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span><span class="o">.+</span> <span class="n">q</span> <span class="o">.*</span><span class="p">((</span><span class="o">-</span><span class="mi">1</span><span class="o">/</span><span class="n">eta</span><span class="p">)</span><span class="o">*</span><span class="n">p</span><span class="o">.^</span><span class="p">(</span><span class="n">eta</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span> <span class="o">.-</span> <span class="n">alpha</span><span class="o">*</span><span class="n">q2</span> <span class="o">.-</span> <span class="n">q</span><span class="o">.^</span><span class="mi">2</span>
+
+
     <span class="k">end</span>
 
     <span class="c"># need a closure around it</span>
     <span class="n">f_closure</span><span class="p">(</span><span class="n">x</span><span class="o">::</span><span class="kt">Vector</span><span class="p">,</span><span class="n">r</span><span class="o">::</span><span class="kt">Vector</span><span class="p">)</span> <span class="o">=</span> <span class="n">resid!</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">r</span><span class="p">,</span><span class="n">p</span><span class="p">,</span><span class="n">basis</span><span class="p">,</span><span class="n">alpha</span><span class="p">,</span><span class="n">eta</span><span class="p">)</span>
     <span class="n">res</span> <span class="o">=</span> <span class="n">nlsolve</span><span class="p">(</span><span class="n">f_closure</span><span class="p">,</span><span class="n">c0</span><span class="p">)</span>
 
-    <span class="c"># plot residual function</span>
-    <span class="n">x</span> <span class="o">=</span> <span class="n">collect</span><span class="p">(</span><span class="n">linspace</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="n">b</span><span class="p">,</span><span class="mi">501</span><span class="p">))</span>
-    <span class="n">y</span> <span class="o">=</span> <span class="n">similar</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-    <span class="n">resid</span><span class="p">(</span><span class="n">res</span><span class="o">.</span><span class="n">zero</span><span class="p">,</span><span class="n">y</span><span class="p">,</span><span class="n">x</span><span class="p">,</span><span class="n">basis</span><span class="p">,</span><span class="n">alpha</span><span class="p">,</span><span class="n">eta</span><span class="p">);</span>
-    <span class="n">figure</span><span class="p">()</span>
-    <span class="n">subplot</span><span class="p">(</span><span class="mi">121</span><span class="p">)</span>
-    <span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span>
-    <span class="n">xlabel</span><span class="p">(</span><span class="s">&quot;price&quot;</span><span class="p">)</span>
-    <span class="n">ylabel</span><span class="p">(</span><span class="s">&quot;residual&quot;</span><span class="p">)</span>
-    <span class="n">title</span><span class="p">(</span><span class="s">&quot;residual function&quot;</span><span class="p">)</span>
-
-    <span class="n">subplot</span><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
-    <span class="n">y</span> <span class="o">=</span> <span class="n">funeval</span><span class="p">(</span><span class="n">res</span><span class="o">.</span><span class="n">zero</span><span class="p">,</span><span class="n">basis</span><span class="p">,</span><span class="n">x</span><span class="p">)[</span><span class="mi">1</span><span class="p">]</span>
-    <span class="n">plot</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="n">x</span><span class="p">,</span><span class="n">label</span><span class="o">=</span><span class="s">&quot;supply 1&quot;</span><span class="p">)</span>
-    <span class="n">plot</span><span class="p">(</span><span class="mi">10</span><span class="o">*</span><span class="n">y</span><span class="p">,</span><span class="n">x</span><span class="p">,</span><span class="n">label</span><span class="o">=</span><span class="s">&quot;supply 10&quot;</span><span class="p">)</span>
-    <span class="n">plot</span><span class="p">(</span><span class="mi">20</span><span class="o">*</span><span class="n">y</span><span class="p">,</span><span class="n">x</span><span class="p">,</span><span class="n">label</span><span class="o">=</span><span class="s">&quot;supply 20&quot;</span><span class="p">)</span>
-    <span class="n">d</span> <span class="o">=</span> <span class="n">x</span><span class="o">.^</span><span class="p">(</span><span class="o">-</span><span class="n">eta</span><span class="p">)</span>
-    <span class="n">plot</span><span class="p">(</span><span class="n">d</span><span class="p">,</span><span class="n">x</span><span class="p">,</span><span class="n">label</span><span class="o">=</span><span class="s">&quot;demand&quot;</span><span class="p">)</span>
-    <span class="n">legend</span><span class="p">()</span>
-    <span class="n">ylabel</span><span class="p">(</span><span class="s">&quot;price&quot;</span><span class="p">)</span>
-    <span class="n">xlabel</span><span class="p">(</span><span class="s">&quot;quantity&quot;</span><span class="p">)</span>
-    <span class="n">title</span><span class="p">(</span><span class="s">&quot;Equilibrium&quot;</span><span class="p">)</span>
-
-
    <span class="c"># plot mS(p) and D(p) for m=1,10,20</span>
 
     <span class="k">return</span> <span class="n">res</span>

diff --git a/Html/mpec-starters.html b/Html/mpec-starters.html
@@ -11928,10 +11928,11 @@ <h3 id="Task-4:-Implement-using-plain-vanilla-NLopt">Task 4: Implement using pla
     <span class="k">function</span> <span class="n">constr</span><span class="p">(</span><span class="n">r</span><span class="o">::</span><span class="kt">Vector</span><span class="p">,</span><span class="n">x</span><span class="o">::</span><span class="kt">Vector</span><span class="p">,</span><span class="n">g</span><span class="o">::</span><span class="kt">Matrix</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">q</span><span class="p">,</span><span class="n">p</span><span class="p">)</span>
         <span class="k">if</span> <span class="n">length</span><span class="p">(</span><span class="n">g</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">0</span>
             <span class="c"># g has to be n by m for nlopt</span>
-            <span class="n">g</span><span class="p">[</span><span class="o">:</span><span class="p">,</span><span class="o">:</span><span class="p">]</span> <span class="o">=</span> 
+            <span class="c"># \partial g_i / \partial x_j</span>
+            <span class="n">g</span><span class="p">[</span><span class="o">:</span><span class="p">,</span><span class="o">:</span><span class="p">]</span> <span class="o">=</span> <span class="n">cat</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">diagm</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="k">end</span><span class="p">]</span><span class="o">*</span><span class="n">ones</span><span class="p">(</span><span class="n">n</span><span class="p">)),</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="p">(</span><span class="n">q</span><span class="o">&#39;.-</span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="o">:</span><span class="p">(</span><span class="k">end</span><span class="o">-</span><span class="mi">1</span><span class="p">)]</span><span class="o">&#39;</span><span class="p">))</span>
         <span class="k">end</span>
         <span class="c"># value of contraints</span>
-        <span class="n">r</span><span class="p">[</span><span class="o">:</span><span class="p">]</span> <span class="o">=</span> <span class="n">value</span> <span class="n">of</span> <span class="n">constraint</span>
+        <span class="n">r</span><span class="p">[</span><span class="o">:</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="k">end</span><span class="p">]</span><span class="o">.*</span><span class="p">(</span><span class="n">q</span><span class="o">.-</span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="o">:</span><span class="p">(</span><span class="k">end</span><span class="o">-</span><span class="mi">1</span><span class="p">)])</span> <span class="o">.-</span> <span class="n">p</span>  <span class="c"># g_i</span>
     <span class="k">end</span>
     <span class="n">constr_clos</span><span class="p">(</span><span class="n">r</span><span class="o">::</span><span class="kt">Vector</span><span class="p">,</span><span class="n">x</span><span class="o">::</span><span class="kt">Vector</span><span class="p">,</span><span class="n">g</span><span class="o">::</span><span class="kt">Matrix</span><span class="p">)</span> <span class="o">=</span> <span class="n">constr</span><span class="p">(</span><span class="n">r</span><span class="o">::</span><span class="kt">Vector</span><span class="p">,</span><span class="n">x</span><span class="o">::</span><span class="kt">Vector</span><span class="p">,</span><span class="n">g</span><span class="o">::</span><span class="kt">Matrix</span><span class="p">,</span><span class="n">N</span><span class="p">,</span><span class="n">demand</span><span class="p">,</span><span class="n">price</span><span class="p">)</span>
 
@@ -12020,6 +12021,7 @@ <h3 id="Task-5:-Implement-using-JuMP">Task 5: Implement using JuMP<a class="anch
 
 
         <span class="c"># define constraints and objective</span>
+
 
 
         <span class="c"># solve</span>