In an optimisation problem, if I have a constraint like g(x) = 0, how do I change it into something like g*(x)

Question

In an optimisation problem, if I have a constraint like g(x) = 0, how do I change it into something like g*(x) <= 0 ?

anonymous · Answer

Actually, I think I'll just set g(x) <= 0 and come up with an extra equation g*(x) = -(g(x)) <= 0, and if the two are satisfied then it means g(x) = 0.

binary3i · Answer

lagrange multipl will help you get other equation

anonymous · Answer

I've forgotten what they are. I think that for this case I won't need anything like that.

I just have that g(x) = 0 defines a line in two dimensions, and I want to have all those equaitons as <= inequalities. So I think I can just sandwich the region as, all x below or on the line, all x above or on the line, and that'll give all the constraints as <= ... seems a bit silly what I'm doing though... I don't know...