Let H(p) be a binary entropy function whose variable p is the difference of 2 probability distributions x and y:



p=sum_i (|x_i-y_i|). That is, f(x,y)=H(p(x,y)).







Q: Given x1,x2,...,xm, find y such that



f(x1,y)*f(x2,y)*...*f(xm,y)



is maximized.



How to solve this problem and what programs can solve this optimization problem.