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!)