# Exercise 30

## Egg carton

Assume your cost function $$J$$ is the following function of two parameters $$(x,y)$$:

$$J(x,y) = -20 e^{A} - e^{B} + 20 + e$$

where

$$A = -0.2 \sqrt{0.5 (x^{2} + y^{2})}$$

and

$$B = 0.5 \left[ \mathrm{cos}(2 \pi x) + \mathrm{cos}(2 \pi y) \right]$$

Map the cost landscape

Compute the cost function $$J$$ for values of $$(x,y)$$ ranging from -10.0 to 10.0, and plot the cost landscape (plot $$J$$ as a function of $$(x,y)$$).

Hint: It should look something like this.

Optimize for (x,y)

Use whatever optimization method you wish, to find the values of $$(x,y)$$ that minimize the cost function $$J$$. Justify that you have found the global minimum and not a local minimum.

Paul Gribble | fall 2014