Turn quadratic minimization to quadratic maximization

Question

Is it possible to change quadratic minimization

$$J_{\text{min}} = \frac{1}{2}x^TQx + c^Tx$$
S.T
$$Ax \leq b$$
$$x \geq 0$$

To quadratic maximization by replacing $$c$$ to $b$ and $Q$ to $A$ just as in linear programming?

$$J_{\text{max}} = -\frac{1}{2}x^TQx + b^Tx$$
S.T
$$A^Tx \leq c$$
$$x \geq 0$$

Answer 1

Minimizing $f(x)$ is equivalent to maximizing $−f(x)$, so $$ \frac{1}{2} x^T Q x + c^T x\to \min \\ \mathrm{s.t.} \begin{cases} Ax \leq b \\ x\geq 0 \end{cases} $$ is the same as $$ -\frac{1}{2} x^T Q x - c^T x = \frac{1}{2} x^T (-Q) x + (-c^T) x\to \max \\ \mathrm{s.t.} \begin{cases} Ax \leq b \\ x\geq 0 \end{cases} $$