## 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 |