# What does "s.t." mean?

English is my second language and I have a question. What does "s.t." mean?

$\text{min} \quad f(x) = (x_1−2)^2+(x_2−1)^2$
$\text{s.t.}\qquad g_{1}(x) = x_{1} - 2x_{2} + 1 = 0$
$\qquad\qquad g_{2}(x) = \frac{x_{1}^2}{4} - x_{2}^2 + 1 \ge 0$

• so that (denotes a condition) 'Minimize $f(x)$ so that $g_1(x) = 0$ and $g_2(x) \geq 0$.' Commented Sep 16, 2014 at 19:56
• I knew "subject to" in an optimization problem formulation and usually "such that" in the other cases.
– Surb
Commented Sep 16, 2014 at 20:03
• (sometimes they use it as "sucht that" as in $\{x: {\rm s.t.\;\; blah})$
– Pedro
Commented Sep 16, 2014 at 20:14
• Abbreviation of "such that". Commented Sep 19, 2014 at 3:42
• And if you want to be even more cryptic, there's a symbol you can use, see tex.stackexchange.com/questions/6282/… Commented Mar 31, 2015 at 2:05

Usually, the acronym $s.t.$ means such that. In the context of optimization, it means subject to. Also note that such that does not have the same meaning as so that.
For clarity, it's usually best to avoid $s.t.$ and simply write such that.
In general mathematics and logic, such that is written as a colon(:), for e.g. $${x^2: \exists n > x \forall n \in \mathbb{N} }$$