Appropriate symbol to denote feasible region I have an optimization problem such as
$$
\min_{x\in\mathop{Range}(\mathbf A) \text{ s.t. } \mathbf B x = b} \|x\|
$$
which I would like to write more concisely as
$$
\min_{x\in\mathcal{X}} \|x\|
$$
where $\mathcal{X} = \{x \in \mathrm{Range}(A) : \mathbf{B}x = b\}$.

What symbol is traditionally used in place of $\mathcal{X}$ to denote the set of feasible $x$?

If the answer depends on whether the constraint set is linear or nonlinear, I am interested in both cases.
Step two1 in "how to do a math problem": label the parts of the problem.  So give the set you want a name.

"Let $S = \{x \in \mathrm{Range}(A) : \mathbf{B}x = b\}$.  ... 
$$  \min_{x \in S} ||x||  $$
... "

1 : The number of this step in any particular "how to do a math problem" may vary.
Step two1 in "how to do a math problem": label the parts of the problem.  So give the set you want a name.

"Let $S = \{x \in \mathrm{Range}(A) : \mathbf{B}x = b\}$.  ... 
$$  \min_{x \in S} ||x||  $$
... "

1 : The number of this step in any particular "how to do a math problem" may vary.