How does one go about proving non-convexity of the function d?
$$ d(v) = 1/2*||F(v)- p||^2 $$
$$ F(v)=\sum_{i=1}^n l_i*\begin{pmatrix} cos(\sum_{j=1}^i v_j) \\ sin(\sum_{j=1}^i v_j \end{pmatrix} $$
$$ F: \Bbb R^n\rightarrow \Bbb R^2, [v,l] \in \Bbb R^n, p \in \Bbb R^2 $$
Proving it by use of the Hessian is not easy, so i figured it would be easier to use the definition of a convex function and a proof by contradiction but so far i've been unable to find a solution.
Observe that $d$ is $2\pi$-periodic in every axial direction. The only way that such a periodic function can be convex is if is constant.