What is the solution of the following optimization problem:

\begin{align} &\min{\mathbf{p}^\mathrm{T} \mathbf{B} \mathbf{p}}\\ &\text{subject to}: \mathbf{0}\leq{\mathbf{p}}\leq \mathbf{1}. \end{align} where ${\mathbf{p}}\in\mathbb{R}^n$ and $\mathbf{B}$ is a symmetric matrix with the elements $b_{ij}\in\{0,+1,-1\}$. Note that $\mathbf{B}$ is not a non-negative definite matrix.

Are there any closed form or approximate solutions? How about upper or lower bounds for the optimal value?

What is the solution of the following optimization problem:

\begin{align} &\min{\mathbf{p}^\mathrm{T} \mathbf{B} \mathbf{p}}\\ &\text{subject to}: \mathbf{0}\leq{\mathbf{p}}\leq \mathbf{1}. \end{align} where ${\mathbf{p}}\in\mathbb{R}^n$ and $\mathbf{B}$ is a symmetric matrix with the elements $b_{ij}\in\{0,+1,-1\}$. Note that $\mathbf{B}$ is not a non-negative definite matrix.

Are there any closed form or approximate solutions? How about upper or lower bounds for the optimal value? (Numerical solutions are not desirable!)

What is the solution of the following optimization problem:

\begin{align} &\min{\mathbf{p}^\mathrm{T} \mathbf{B} \mathbf{p}}\\ &\text{subject to}: \mathbf{0}\leq{\mathbf{p}}\leq \mathbf{1}. \end{align} where ${\mathbf{p}}\in\mathbb{R}^n$ and $\mathbf{B}$ is a symmetric matrix with the elements $b_{ij}\in\{0,+1,-1\}$. Note that $\mathbf{B}$ is not a non-negative definite matrix.

Are there any closed form, approximate solution or bounds for the optimal value?

What is the solution of the following optimization problem:

\begin{align} &\min{\mathbf{p}^\mathrm{T} \mathbf{B} \mathbf{p}}\\ &\text{subject to}: \mathbf{0}\leq{\mathbf{p}}\leq \mathbf{1}. \end{align} where ${\mathbf{p}}\in\mathbb{R}^n$ and $\mathbf{B}$ is a symmetric matrix with the elements $b_{ij}\in\{0,+1,-1\}$. Note that $\mathbf{B}$ is not a non-negative definite matrix.

Are there any closed form or approximate solutions? How about upper or lower bounds for the optimal value?