Is this optimization problem called unconstrained quadratic program?

Question

\begin{equation} \arg\min_{c} \frac{1}{2}c^TAc + f^Tc \end{equation} where $A$ is a symmetric $n\times n$ matrix, $f$ and $c$ are vectors in $\mathbb{R}^n$. Can we call this problem an unconstrained quadratic program?

Answer 1

Yes.

Note that depending on whether or not $A$ is positive semidefinite, the problem might be convex or it might be non-convex. If it is non-convex, then the minimization is unbounded.