I am working on a problem involving a non-convex quadratically-constrained quadratic program and am seeking efficient algorithms to find its global minimum. The problem is structured as follows:

Fix some natural numbers $I,J\geq2$ and let $K=I+J+2IJ$. Fix some $(c_1,\ldots,c_I)\in(0,1)^I$ such that $\sum_{i=1}^{I}c_i<1$. The problem is given by
\begin{align*}
	\underset{\mathbf{x}\in\mathbb{R}^K}{\text{minimize}}&\quad\frac{1}{2}\mathbf{x}^T\mathbf{P}_0\mathbf{x}+\mathbf{q}_0^T\mathbf{x}\\
	\text{subject to}&\quad\frac{1}{2}\mathbf{x}^T\mathbf{P}_m\mathbf{x}+\mathbf{q}_m^T\mathbf{x}+r_m\leq0,\quad\forall m\in\mathcal{M}\subseteq\mathbb{N} \\
	&\quad\mathbf{A}\mathbf{x}=\mathbf{b}
\end{align*}
where the index set for the inequality constraints $\mathcal{M}$ can be partitioned into four cells, denoted $\mathcal{M}_1$, $\mathcal{M}_2$, $\mathcal{M}_3$, and $\mathcal{M}_4$, respectively. The properties of the coefficients are as follows.

 1. For the objective function, we have
	$$
		\mathbf{P}_0=
		\begin{pmatrix}
			\mathbf{I}_J & \mathbf{0} \\
			\mathbf{0} & \mathbf{0}
		\end{pmatrix}
	$$ß
	positive semi-definite, and
	$$
		\mathbf{q}_0=-(q_{01},\ldots,q_{0J},0,\ldots,0)^T
	$$
	where $(q_{01},\ldots,q_{0J})\in\Delta(\{1,\ldots,J\})$.
	

 2. We have four sets of inequality constraints.
     - For $m_{1k}\in\mathcal{M}_1$ with $k\in\{1,\ldots,K\}$, we have
		$$
		\mathbf{P}_{m_{1k}}=\mathbf{0},
		\quad
		\mathbf{q}_{m_{1k}}=-\mathbf{e}_k,
		\quad\text{and}\quad
		r_{m_{1k}}=0,
		$$
		where $\mathbf{e}_k$ denotes the $k$-th standard unit vector for $\mathbb{R}^K$.
    - For $m_{2i}\in\mathcal{M}_2$ with $i\in\{0,1,\ldots,I\}$, we have
		$$
		\mathbf{P}_{m_{2i}}=\mathbf{0},
		\quad
		\mathbf{q}_{m_{2i}}=
		\begin{pmatrix}
			\mathbf{e}_{i+1}\otimes\mathbf{\iota}_J \\
			\mathbf{0}
		\end{pmatrix},
		\quad
		r_{m_{20}}=-1,
		\quad\text{and}\quad
		r_{m_{2i}}=-c_i\ \forall i>0,
		$$
		where $\mathbf{e}_{i+1}$ denotes the $(i+1)$-th standard unit vector for $\mathbb{R}^{I+1}$, and $\mathbf{\iota}_J$ denotes the $J$-vector of ones.
    - For $m_{3ij}\in\mathcal{M}_3$ with $i\in\{1,\dots,I\}$ and $j\in\{1,\ldots,J\}$, we have
		$$
		\mathbf{P}_{m_{3ij}}=\mathbf{E}_{s(i,j),t(i,j)},
		\quad
		\mathbf{q}_{m_{3ij}}=\mathbf{0},
		\quad\text{and}\quad
		r_{m_{3ij}}=0,
		$$
		where $\mathbf{E}_{st}$ denotes the matrix unit with the nonzero entry at the $s$-th row and $t$-th column, with $s(i,j)=j+iJ$ and $t(i,j)=j+iJ+I+J+IJ$. $\mathbf{E}_{s(i,j),t(i,j)}$ is indefinite for all $i,j$.
    - For $m_{4i}\in\mathcal{M}_4$ with $i\in\{1,\ldots,I\}$, we have 
		$$
			\mathbf{P}_{m_{4i}}=
			\begin{pmatrix}
				\mathbf{e}_{i+1}\otimes\mathbf{\iota}_J \\
				\mathbf{0}
			\end{pmatrix}
			\mathbf{e}_{i+(I+1)J}^T,
			\quad
			\mathbf{q}_{m_{4i}}=-c_i\mathbf{e}_{i+(I+1)J}
			\quad\text{and}\quad
			r_{m_{4i}}=0,
		$$
		where $\mathbf{e}_{i+(I+1)J}$ denotes the $(i+(I+1)J)$-th standard unit vector for $\mathbb{R}^K$, and $\mathbf{e}_{i+1}$ denotes the $(i+1)$-th standard unit vector for $\mathbb{R}^{I+1}$.

3. For the equality constraints, we have
	$$
		\mathbf{A}=
		\begin{pmatrix}
			\mathbf{\iota}_I\otimes\mathbf{I}_J & \mathbf{0} & \mathbf{I}_I\otimes\mathbf{\iota}_J & -\mathbf{I}_{IJ}
		\end{pmatrix}
		\in\mathbb{R}^{IJ\times K}
		\quad\text{and}\quad
		\mathbf{b}=
		\begin{pmatrix}
			\mathbf{b}_1 \\
			\vdots \\
			\mathbf{b}_I
		\end{pmatrix}
	$$
	where $\mathbf{b}_i\in\Delta(\{1,\ldots,J\})$ for all $i=1,\ldots,I$.

Any pointers to relevant literature and algorithms would be very helpful. Thanks a lot!