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 $2x\geq 0$.

  • $\begingroup$ But then defining $x \in \mathbb{R}_+$ would have been so much better. So also I'm not sure :) $\endgroup$ – independentvariable Mar 29 at 21:03

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