title: Error in solve.default(oout$hessian) : Lapack routine dgesv: system is exactly singular: U[1,1] = 0
body: <p>I am using the maximum likelihood method to estimate a set of parameters. Now I am going to use  <code>mle</code> function from the <code>stats4</code> package in R to make a profile likelihood for one of the parameters. To do that, I need to fix one of the parameters when I call the <code>mle</code> function. Here is the code:</p>
  <pre><code>fr &lt;- function(x1, x2, x3) {   
    100 * (x2 - x1 * x1)^2 + (1 - x1)^2 + x3
  }
  
  out &lt;- mle(fr,start = list(x1=1, x2=2, x3=3), method=&quot;Nelder-Mead&quot;,
             control=list(trace=4), fixed = list(x2=1))
  </code></pre>
  <p>and I get this error:</p>
  <blockquote>
  <p>Error in solve.default(oout$hessian) :
  Lapack routine dgesv: system is exactly singular: U[1,1] = 0</p>
  </blockquote>
  <p>If I do not use the <code>fixed</code> option, then I do not have this error, but the result is not a profile likelihood. Can you please let me know how can I solve this issue?</p>