# 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 $g_2(x) \geq 0$.' – flawr Sep 16 '14 at 19:56
• I knew "subject to" in an optimization problem formulation and usually "such that" in the other cases. – Surb Sep 16 '14 at 20:03
• (sometimes they use it as "sucht that" as in $\{x: {\rm s.t.\;\; blah})$ – Pedro Tamaroff Sep 16 '14 at 20:14
• Abbreviation of "such that". – Fujoyaki Sep 19 '14 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/… – Robert Soupe Mar 31 '15 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. $${x^2: \exists n > x \forall n \in \mathbb{N} }$$