I want to find an optimal solution $X=[x_1, x_2, x_3, x_4, x_5]$, for $x_i\in\mathbb{R}^n$, that minimizes $$ f(X) = \lVert y_1-x_1 \rVert^3 + \lVert y_2-x_2 \rVert^3 + \lVert y_3-x_3 \rVert^3 + \lVert x_1-x_5 \rVert^3 + \lVert x_2-x_4 \rVert^3 + \lVert x_3-x_5 \rVert^3 + \lVert x_4-x_5 \rVert^3, $$ where $y_1$, $y_2$, and $y_3$ are given vectors.
I failed to prove that the objective function $f(X)$ is convex, and I am roughly guessing $f(X)$ is a non-convex function.
Please recommend me some material, subjects, algorithms, or whatever related to this problem form. Thank you for reading my question.