TITLE: What does "s.t." mean?
QUESTION [30 upvotes]: English is my second language and I have a question. What does "s.t." mean?
$ \text{min} \quad f(x) = (x_1−2)^2+(x_2−1)^2 $ 
$ \text{s.t.}\qquad g_{1}(x) = x_{1} - 2x_{2} + 1 = 0 $ 
$ \qquad\qquad g_{2}(x) = \frac{x_{1}^2}{4} - x_{2}^2 + 1 \ge 0 $

REPLY [6 votes]: Usually in optimization problems s.t. is written to denote subject to because, an optimization problem is usually of the form:
Optimize f(x) subject to the constraint g(x)
In general mathematics and logic, such that is written as a colon(:), for e.g.
$${x^2: \exists n > x \forall n \in \mathbb{N} }$$