Turn quadratic minimization to quadratic maximization

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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 $$A^Tx \leq c$$ $$x \geq 0$$

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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 $$ -\frac{1}{2} x^T Q x - c^T x = \frac{1}{2} x^T (-Q) x + (-c^T) x\to \max \\ \mathrm{s.t.} \begin{cases} Ax \leq b \\ x\geq 0 \end{cases} $$