# How to minimize a function using vectors as input?

I'm learning Mathematica and meet a problem. Here is a simple example.

x = {0, 0.5, 1}
y = {a-3,b,10}
yl= {b,a,5}


I want to find the value of a and b when it minimum of (y-x)^2+(yl-x)^2

Nminimize[(y - x)^2 + (yl - x)^2, {a,b}]


But it returns

Minimize[{(-3. + a)^2 + (0. + b)^2, (-0.5 + a)^2 + (-0.5 + b)^2, 97.}, {a, b}]


What's the right way to solve this problem? Thanks

• I don't think I understand this at all. When a is 1, y1 - y is zero right? Apr 9, 2020 at 18:11
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• Can you give a minimal example of what you are trying to do? This is not clear enough for people to help you. Apr 9, 2020 at 18:49
• Also note that NMinimize is case sensitive and you are showing Nminimize. Apr 9, 2020 at 18:53
• I rewrite the example, I think it is clear now, thank you guys
– YzWu
Apr 9, 2020 at 18:59

You have a typo in NMinimize and it will require the objective function to be a scalar and not a vector. You could minimize the Norm of the vector like so.
x = {0, 0.5, 1};