TITLE: What does "subject to" mean in math?
QUESTION [5 upvotes]: For instance, I saw the expression in the Wikipedia article on Lagrange multipliers:

maximize $f(x, y)$
  subject to $g(x, y) = c$

What does "subject to" mean?

REPLY [14 votes]: It is a way to specify constraints. To put it very simply, the problem 
"do 'X' subject to 'Y'" means that, you have to do "X" (whatever X is), but you have to do it such that "Y" is also satisfied in the process.
As an example, in 1-D

"minimize $x^2$" would just give the answer $0$; but
"minimize $x^2$ subject to $x \geq 10$ would yield the answer $100$, since you cannot consider $x < 10$ in your problem.