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 $
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asked Sep 16, 2014 at 19:55
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1$\begingroup$ so that (denotes a condition) 'Minimize $f(x)$ so that $g_1(x) = 0$ and $g_2(x) \geq 0$.' $\endgroup$– flawrSep 16, 2014 at 19:56
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4$\begingroup$ I knew "subject to" in an optimization problem formulation and usually "such that" in the other cases. $\endgroup$– SurbSep 16, 2014 at 20:03
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2$\begingroup$ (sometimes they use it as "sucht that" as in $\{x: {\rm s.t.\;\; blah})$ $\endgroup$– Pedro ♦Sep 16, 2014 at 20:14
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3$\begingroup$ Abbreviation of "such that". $\endgroup$– FujoyakiSep 19, 2014 at 3:42
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1$\begingroup$ And if you want to be even more cryptic, there's a symbol you can use, see tex.stackexchange.com/questions/6282/… $\endgroup$– Robert SoupeMar 31, 2015 at 2:05
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2 Answers
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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.
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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. $${x^2: \exists n > x \forall n \in \mathbb{N} }$$
