I'm attempting to solve a constrained optimization problem via Kuhn-Tucker, and I'm being asked to write the necessary conditions for some point $x$ to be a solution.
The part of the K-T theorem stating the necessary conditions for a solution assume that the objective function $f$ is concave, and that the constraint functions $g_k$ are concave. My question is, what does it mean for a constraint to be concave? For example, one of the constraints in this problem is that $x\geq0$, but I only understand concavity to be describing a function taking singleton values over some set, not describing the set itself.
Best Answer
Here, your constraint function is $g(x)=x$, and your constraint is $g(x)\geq 0$. $g$ is a concave (but not strictly concave) function. So, you meet the KKT conditions, as long as $f$ is concave, and as long as your other constraint functions are concave.