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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 $

Widawensen
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Heniek Kowalski
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    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
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    I knew "subject to" in an optimization problem formulation and usually "such that" in the other cases. – Surb Sep 16 '14 at 20:03
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    (sometimes they use it as "sucht that" as in ${x: {\rm s.t.;; blah})$ – Pedro Sep 16 '14 at 20:14
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    Abbreviation of "such that". – Fujoyaki Sep 19 '14 at 03:42
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    And if you want to be even more cryptic, there's a symbol you can use, see http://tex.stackexchange.com/questions/6282/how-do-i-make-the-such-that-symbol-from-set-theory – Robert Soupe Mar 31 '15 at 02:05
  • Sort of unrelated, but I have also seen "STS" or "s.t.s." used for "suffices to show". I write this here in case people searching for "sts" will come across this thread. – D.R. Oct 27 '23 at 07:28

2 Answers2

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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.

Such that, describes how something should be done.

So that, describes why something should be done.

For clarity, it's usually best to avoid $s.t.$ and simply write such that.

k170
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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. $${x^2: \exists n > x \forall n \in \mathbb{N} }$$

Satya
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