# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

## MAT 168: Optimization

**Approved:**2003-03-01 (revised 2013-01-01, M. Koeppe)

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

Search by ISBN on Amazon: 978-1441944979

**Prerequisites:**

**Suggested Schedule:**

Lecture(s) |
Sections |
Comments/Topics |

Week 1 |
Chapter 1 (*) |
Modelization: Examples, equivalence between various formulation (includes introduction to modeling languages). |

Week 2-3 |
Chapters 2, 4, and 6 |
The Simplex Method: Pivoting, finite termination. Applications: Inventory, manufacturing, curve fitting. Transportation problems: Special version of the simplex method (includes setting up individual work projects). |

Week 4 |
Chapters 5 and 9 |
Duality for linear programs. Interpretation of dual problem, variables. |

Week 5 |
Chapter 7 |
Sensitivity analysis with respect to the resource vector, cost. |

Week 6 |
Chapter 3 |
The geometry of linear programs: Polyhedral convexity. |

Week 7-8 |
Chapters 16 and 17 |
Interior point methods: Optimality conditions, the Newton-Raphson Method for systems of (nonlinear) equations, primal-dual interior point method. |

Week 9-10 |
Chapters 13 and 14 |
Network flow problems: minflow/Max-cut Theorem, algorithmic procedures for solving network flow problems. Applications to communication, distribution, project scheduling. |

**Additional Notes:**

**Learning Goals:**

**Assessment:**