You can use the partial derivate to find the minimum(relative)/maximum(relative) of a function , In this case the function is:

If you draw a graphic for this problem, you can see that in this case the function only has a minimum and this point is an absolute minimum. Something like this:

Then: For find X such that f(X, Y) is minimum(absolute minimum in this problem)

1. Derivate f(X, Y) respect of X (consider Y as a constant)
2. Make the result equal to zero
3. Find X in the new equation and replace all x[i], w[i]. (You should have the value of X)

The same steps for Y, finally evaluate (X, Y) in f(X, Y) and obtain the final answer.

The final complexity is O(n). Good luck.

PD.: Sorry for my poor english.