Optimize Of Quadratic Polynomial

#1

Why we take Square of Error Instead of Modulus Operation in Optimization Problems??

#2

Having a square as opposed to the absolute value function gives a nice continuous and differentiable function (absolute value is not differentiable at 0) - which makes it the natural choice, especially in the context of estimation and regression analysis.
Because we have to minimize the error and finding minima of a differentiable functions is pretty straightforward

#3

Also, by squaring, large differences are emphasized.(Think of the effect outliers would have). Apart from amplifying large differences, squaring also minimizes tiny differences.

#4

Modulus function is also continuous and differentiable .
(Square value non differentiable at tangent or mima).

Finding mima will be easy in squared function agree.YES

As E = |y-h(x)| find min value of h(x) may be difficult.
h(x) = mx+c