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 $

Solution 1:

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.

Solution 2:

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