I'm using an ellipsoid $f = x^a + |y|^b + |z|^c - 1 = 0$ to fit some data (a failure envelope), where $x \in [0, 1]$, $y \in [-1, 1]$, and $z \in [-1, 1]$ are all normalized variables and $a$, $b$, $c$ are to-be-optimized coefficients. The fitting is not good, so I decided to add some coupling terms into $f$, including symmetric terms such as $d_1x^{d_2}|y|^{d_3}$ and also asymetric terms such as sign($z$)$e_1x^{e_2}|z|^{e_3}$.
Ten coupling terms were added into $f$ (let's call it $f^*$). During optimizaiton, I didn't put any constraint. So, occasionally, the optimal coefficients may result in overshooting, such as $x > 1$, which is prevented.
My question is what constraints should I put to the coefficients to retain $f^*$ being valid. Or what general principles should I follow to design the constraints? Thanks.