How to solve minimize sum_k 1norm(x-x_k)^2 * norm(y-y_k)^2, where x,y,x_k,y_k are vectors with the same length, can we use CVX to solve this problem, thank you

Nonconvex
2

You didn’t say, but I’ll presume x and y are the optimization variables.

That doesn’t look convex to me. So no.