I have a non linear problem to solve which is something like (just to give a rough idea)
$$ \begin{array}{l} \min \sum_{k=1}^{n} z_k^2 \\ \text{s.t.} \\ \lVert p_i - p_j \rVert_2^2 = \text{constant}_{ij} \\ x_iy_j - y_ix_j \geq 0 \end{array} $$
here $p_i = (x_i,y_i,z_i)$, I'm reading through a numerical optimization book to try at least to classify the problem, but it seems to me I can only use some SQP solver, is there anything else you can suggest?
I'm pretty sure this problem doesn't have a unique solution, but I have the feeling these solution would be somehow equivalent, so finding a local minimum should be fine.