Suppose there is a optimization problem that aims at minimizing an objective function $X$ but we can't develop a mathematical model for minimizing $X$. However, there are two objective functions $Y$ and $Z$, where $Y$ and $Z$ are a lower bound and an upper bound of $X$ respectively. We can develop a mathematical model for minimizing either $Y$ or $Z$. Then $X$ is calculated for the output solution hoping that the solution with $Y_\min$ (or $Z_\min$) will have an $X$ value with a good deviation from $X_\min$ (which is unknown).
Is there any theoretical theory that states which is better: to minimize w.r.t $Y$ (the lower bound) or w.r.t $Z$ (the upper bound) if we can't minimize w.r.t to $X$?