Is there any closed form solution for the optimal value of the folowing optimization problem?

$$\begin{array}{ll} \text{minimize} & (\mathbf{x} - \mathbf{y})^{\mathrm{T}}\mathbf{B}(\mathbf{x} - \mathbf{y}) + \mathbf{1}^{\mathrm{T}} \mathbf{y} \\ \text{subject to} & \mathbf{x}, \mathbf{y} \geq \mathbf 0\end{array}$$

where $\mathbf{1}$ is an all-one vector and $\mathbf{B}$ is a symmetric indefinite matrix.