I am reading Boyd's Convex Optimization textbook and I am looking at example 3.22, line 2.
It says $y^T x - \frac12 x^T Q x$ is bounded from above for all possible values of $y$. Also, it is important to note $Q$ is a symmetric positive definite. So for all values of $x$, $x^T Q x$ is a positive number. Why is $y^T x - \frac12 x^T Q x$ bounded above? I am not sure how to compare the quantity $y^T x$ with the quantity $\frac12 x^T Q x$. For $y=0$, I can see why.. then there are two cases, $y>0$ and $y<0$.