How to find least-mean-square error quadratic upper bound?
<p>I have some data of the form</p>

<p><code>x1[i], x2[i], x3[i], z[i]</code>,</p>

<p>where <code>z[i]</code> is an unknown deterministic function of <code>x1[i], x2[i], and x3[i]</code>.  I would like to find a quadratic function <code>u(x1, x2, x3)= a11*x1^2 + a22*x2^2 + a33*x3^2 + a12*x1*x2 + ... + a0</code> that overbounds the data, i.e., <code>u(x1[i], x2[i], x3[i]) &gt;= z[i]</code> for all <code>i</code>, and that minimizes the sum of the squared errors subject to the constraints.  </p>

<p>Is there a computationally efficient solution approach in either Python or Matlab?</p>