I need to find \begin{equation} \mathbf{d}_i=\max \;( \sum_i \Vert \mathbf{P}x_i \Vert_2^2 ) \;\;s.t.\;\; \Vert \mathbf{d}_i\Vert=1 \end{equation} where $\mathbf{P}$ is the projection operator i.e., $\mathbf{P=DD^+}$, $+$ being the pseudo inverse operator, $\mathbf{d}_i$ is a column of $\mathbf{D} \in \mathbb{R}^{n\times d}$, $\mathbf{d}_i \;\&\; \mathbf{x}_i \in \mathbb{R}^n$.
How to do this using Lagrange multiplier method?