What is wrong with my explanation of the convex problem concept?

Question

The question is: Explain the concept of a convex optimization problem.

My answer: A convex optimization problem is a problem where all of the constraints are convex functions, and the objective function is a convex function.

Comment from examiner: Not really 1.5/2.0.

Why didn't my answer give full credits? What am I missing, I thought this was the definition of a convex optimization problem. I am genuinely curious.

Answer 1

I think you should better ask the examiner directly, if possible.

The precise answer depends on the definition of a convex optimization problem, which can vary.

For example, some people define a convex optimization problem as a problem where the objective function is convex and the feasible set is convex. Note that this is not the same as your answer, because one can describe a convex feasible set with functions that are not convex.

Answer 2

Your answer is missing two things:

1. That the objective is to be minimized (or maximized if the objective function is concave).
2. That the convex function in the constraint has to be at the left side of the "$\leq$".