Consider optimization problem $$ \max_x f(x) $$ $x$ could be of any dimension.
Question 1: There is only one constraint $g(x)\ge 0$.
Question 2: There are two constraints $g(x)\ge 0, h(x)\ge 0$.
Suppose I can show that $h(x)\ge 0$ is always binding in question 2. Is there any relationship between the binding-slackness of $g(x)\ge 0$ in question 1 and 2?
For instance, can we show that $g(x)=0$ in question 1 implies $g(x)=0$ in question 2, or vice versa?
If not, what additional assumptions do I need to make it happen?
Thanks a lot!