Suppose $x_i \in\mathbb{R}^2$ for $i=1,2,...9$ are unknown. I'm given the pair-wise distance matrix between these points $D$ which is a $9*9$ symmetric matrix. I want to learn these data points by minimizing the following loss function over $x_1,\ldots x_9$
$$\sum\limits_{i,j}(\|x_i - x_j\|_2 - D_{ij})^2 $$
How can learn the data points? I know that I can fix the first two points such that distance between them is same as $D_{12}$, but not sure how to proceed from there.
How can I use this to do some kind of simultaneous gradient descent?