where a,b,c and d are observed/registered variables for each sample i.

x1,x2,x3 and x4 are unknowns and will be same for all samples (i.e. all i's).

I've lot of samples say n (at least more than the number of unknowns i.e. n>4) and thus I've a host of equations

from all samples (n samples => n equations) with four unknowns in each sample's equation.

My objective is to get optimum value of x1,x2,x3 and x4 so that with these values of unknowns, all w will fall as close as possible.

In other word w(1)~w(2)~w(3)~....w(n-1)~w(n) with optimum values for x1,x2,x3 and x4.

Can you suggest me some solution/hint. Please.