I am newbie in optimization problem, I have the following optimization problem: $$\max \quad \frac{1}{2}x^THx - q^THx$$ $$\text{s.t.} \;\;l\leq x \leq u$$ where $H, q$ are known constants, and H is positive semi-definite, then it's a non-convex problem. I need to reformulate in a standard form (non-convex): $$\min \quad \frac{1}{2}x^THx + f^Tx$$ $$\text{s.t.} \quad Ax \leq b, \;\;A_{eq}x=b_{eq}, \;\;l\leq x \leq u$$ Where H is not positive semidefinite.
My first intuition, I hope it's the right one, it was to multiply by -1 the first optimization problem: $$\min \quad \frac{1}{2}x^TVx + f^T x$$ $$\text{s.t.} \;\;l\leq x \leq u$$ where $V = -H$ and $f = -q^TV$, so my question, is it correct? or which will it be correct reformulation?