the problem of approximating m data points $(x_i, y_i)$ in $r^n+1$, with a quadratic function $q(x,p)$ with s parameters $s<=m$, is considered. the parameter vector $p$ in $r^s$ is determined so as to satisfy three conditions: (1) $q(x,p)$ must underestimate all m data points, i.e. $q(x_i,p)<=y_i$, $i=1,....m$. (2) the error of approximation is to be minimized in the $l1$ norm. (3) the eigenvalues of $h$ are to satisfy specified lower and upper bounds, where $h$ is the hessian of $q(x,p)$ with respect to $x$. approximation of the data by a sum of negative gaussians is also considered.