What kind of optimization problem is $f(x) = \frac{1}{2}x^TAy$

Question

Let $y \in \mathbb{R}^n$ be an arbitrary vector.

What type of optimization question is

$$f(x) = \dfrac{1}{2}x^TAy$$

where we seek to minimize $x$ over $\mathbb{R}^n$. I know it is not a QP. Is it just a linear program? The fact we have an $A$ matrix makes me uncertain

What are the conditions for convexity?

Answer 1

This is a convex and linear optimization problem. It is solvable if and only if $Ay=0$.