# 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 $$J$$.

Paul Gribble | fall 2014 