I have a minimizing problem.

$$\min y$$ $$xQx'=y$$ $$0\leq x_i\leq1$$ $$Az\leq b$$ where $Q$ is diagonal and has positive diagonal integer values and $A\in\mathbb Z^{m\times n}$ and $b\in\mathbb Z^m$ are constant matrix and vector respectively while $z\in\mathbb R^n$ is variables that contain $x_1,\dots,x_t,y\in\mathbb R$ as well.

Is this problem $NP$-hard or solvable in polynomial time?

I have the following minimization problem in $z \in \mathbb R^n$, which contains $x_1, \dots, x_t, y \in \mathbb R$.

$$\begin{array}{ll} \text{minimize} & y\\ \text{subject to} & xQx'= y\\ & 0 \leq x_i \leq1\\ & Az \leq b\end{array}$$

where $Q$ is diagonal and has positive diagonal integer values, $A \in \mathbb Z^{m \times n}$ and $b \in \mathbb Z^m$ are given.

Is this problem $NP$-hard or solvable in polynomial time?

I have a minimizing problem.

$$\min y$$ $$xQx'=y$$ $$0\leq x_i\leq1$$ $$Az\leq b$$ where $Q$ is diagonal and has positive diagonal values and $A\in\mathbb R^{m\times n}$ and $b\in\mathbb R^m$ are constant matrix and vector respectively while $z\in\mathbb R^n$ is variables that contain $x_1,\dots,x_t,y\in\mathbb R$ as well.

Is this problem $NP$-hard or solvable in polynomial time?

I have a minimizing problem.

$$\min y$$ $$xQx'=y$$ $$0\leq x_i\leq1$$ $$Az\leq b$$ where $Q$ is diagonal and has positive diagonal integer values and $A\in\mathbb Z^{m\times n}$ and $b\in\mathbb Z^m$ are constant matrix and vector respectively while $z\in\mathbb R^n$ is variables that contain $x_1,\dots,x_t,y\in\mathbb R$ as well.

Is this problem $NP$-hard or solvable in polynomial time?