title: Why Mathematica FindMinimum does not return the optimal solution for Vectors?
body: <p>I want to use Mathematica <strong>FindMinimum</strong> method for optimalization of a Vector (Q). Specifically I want to minimize the entropy <strong>-Total(Q*Log[Q])</strong> subject to the constraint <strong>Total[Q]dx == 1</strong> and <strong>Total[Qx]dx == 0.2</strong>.
  The result should be an exponential function in Q.</p>
  <p>Here is the code I used:</p>
  <pre><code>NUMx = 49
  x = N@Subdivide[0, 5, NUMx];
  dx = x[[2]] - x[[1]];
  FindMinimum[{-Total[Q*Log[Q]]*dx, Total[Q]*dx == 1, 
    Total[Q*x]*dx == 0.2, Q \[Element] Vectors[NUMx, PositiveReals], 
    Q &gt; 10^-8}, Q, Method -&gt; &quot;InteriorPoint&quot;]
  </code></pre>
  <p>But it returns:</p>
  <pre><code>{0.32588, {Q -&gt; {0.0156863, 0.0156863, 0.0156863, 0.0156863, 
      0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 
      0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 
      0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 
      0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 
      0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 
      0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 
      0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 0.0156863, 
      0.0156863, 0.0156863, 0.0156863, 0.0156863}}}
  </code></pre>
  <p>How should I proceed to get the correct results?</p>