title: Optimization in R - nonlinear utility function with non-linear constraints
body: <p>Am trying to find vector <code>β</code> to maximize function </p>
  
  <p><img src="https://i.stack.imgur.com/JjQou.jpg" alt="enter image description here"></p>
  
  <p>subject to 
  (a) </p>
  
  <p><img src="https://i.stack.imgur.com/XUEQR.jpg" alt="enter image description here"></p>
  
  <p>and
  (b) all elements of  <code>β</code> should be non-negative, </p>
  
  <p>with <code>β, μ</code> are vectors of length 15, and <code>M</code> is a 15x15 covariance matrix (<code>μ</code> and <code>M</code> are given).</p>
  
  <p>Any advice on which of the optimizers listed on <a href="http://cran.r-project.org/web/views/Optimization.html" rel="nofollow noreferrer">Stefan Theussl's CRAN page</a> would be most suited for my case?</p>