Hi. I'm trying to minimize the distance between two sets by scaling one set. (I guess this can really be thought as the distance between two functions.) For example:

Set A = {2, 2, -4, 1}

Set B = {1, 1, -2, .0001}

So I want to minimize the following distances using a scale factor x:

d1 = 2 - x

d2 = 2 - x

d3 = -4 + 2x

d4 = 1 - .0001x

I'm really stumped! The answer should obviously be ~2, but I can't seem to figure out how to get there. Using the average x is way off (I introduced the .0001 to illustrate this). Can anyone help? Thx