# How many constraints are there in $g(x) \leq 2x \geq 0$?

How many constraints are there in $$g(x) \leq 2x \geq 0$$?

I thought $$g(x) \leq 2x$$ and $$g(x) \geq 0$$, but something suggested that there could be three rather than two constraints here?

Perhaps the third one is about constraining $$2x$$ from above?

The reason for there being third one is that this is in a "black box optimization" example. And the author evaluates three distinct inequality constraints. Rather than two.

Third one could be $$2x - g(x) \geq 0$$, but I'm not sure if this makes any difference? Shouldn't this be captured by the two constraints already? Unless one must make sure that $$2x \geq 0$$?

I'd say it's not clearly written, and I would advise anyone writing constraints that way to stop it. But if I had to intepret it, I would say the constraints are $$g(x)\leq 2x$$ and $$2x\geq 0$$.
• But then defining $x \in \mathbb{R}_+$ would have been so much better. So also I'm not sure :) – independentvariable Mar 29 at 21:03