## Week 12: November 16 - 20

### Multivariable Optimization

We extend our study of optimization techniques to problems where more than one variable can be changed at a time.

### Global Positioning System (GPS)

Finding a location using the Global Positioning System (GPS) can be formulated as a multivariable optimization problem. Using a simplified 2D GPS model, we solve this problem using the techniques developed in class.

Week 12 Notebook

## Quiz 6

• meshgrid
• polar
• hist
• Axis-dependent operations: sum, mean, amax, amin
• random.rand
• random.normal
• legend
• contour
• contourf
• colorbar
Sample Quiz 6

## Assignment 9: Global Positioning System

Activity:

• Describe and implement the "stumble down" optimization algorithm discussed in class.
• Explain how GPS works.
• Apply the "stumble down" algorithm with reducing step sizes to find the optimum location for the 2D version of the GPS problem to 8 significant figures.
• Plot the steps taken by the "stumble down" algorithm as it approaches the minimum, and the final location.

### Section 000 Measurements

Satellite X coordinate Y coordinate Distance
Recalculate 553 223 272
Westboro Baptist Church 444 845 363
Pyrite 4.5 38.1 675
Alexander Hamilton 667 562 177

### Section 100 Measurements

Satellite X coordinate Y coordinate Distance
Death Star 412.5 257.7 251.6
Mr Satellite 580 876 397
Grofflesby 438 750 270.5
XYZ 359.2 658.8 222.6