Exercise 27
Here the idea is to take a cost function \(J\) and in a brute-force way, map out the entire cost landscape — that is, how \(J\) varies across a broad range of parameter values.
1D cost landscape
Assume that the cost function \(J\) is a function of a single parameter \(x\):
\begin{equation} J = x e^{(-x^{2})} + \frac{x^{2}}{20} \end{equation}Map J
Assume values of \(x\) range between -10.0 and +10.0. Generate a plot of the cost function \(J\) over this range.
Optimize x
Use an optimization method of your choosing to find the value of \(x\) that minimizes \(J\).
2D cost landscape
Assume that the cost function \(J\) is a function of two parameters \(x\) and \(y\):
\begin{equation} J = x e^{(-x^{2}-y^{2})} + \frac{x^{2}+y^{2}}{20} \end{equation}Map J
Assume values of \(x\) and \(y\) both range between -3.0 and +3.0. Generate a plot of the cost function \(J\) over this range.
Optimize (x,y)
Use an optimization method of your choosing to find the \((x,y)\) pair that minimizes \(J\).
