Cost Landscapes

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 \(x\):

\[ J = x e^{(-x^{2})} + \frac{x^{2}}{20} \]

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 \(y\):

\[ J = x e^{(-x^{2}-y^{2})} + \frac{x^{2}+y^{2}}{20} \]

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 \(J\).

sample solution