#### Prerequisites & Bulletin Description

#### Course Objectives

The main objective of Mathematics of Optimization is to introduce linear optimization models, their solution techniques, and interpretation of their solutions. Specifically, students wil be able to

- Model an optimization problem as a linear program and solve using the simplex method.
- Interpret the solutions of simplex algorithm in order to perform sensitivity analysis.
- Model various convex optimization problems as semidefinite programs and solve them using an appropriate interior point method.
- Model discrete optimization problems as integer programs and solve them using cutting plane and branch-and-bound methods.

#### Evaluation of Students

Students will demonstrate their mastery of the course objectives on frequent graded homework assignments, midterm and final examinations.

#### Course Outline

Topics |
Number of Weeks |

Linear programming and simplex algorithm | 7 |

Semidefinite programming and interior point algorithms | 4 |

integer programming and cutting plane/branch-and-bound algorithms | 4 |

#### Textbook

*Introduction to Linear Optimization* by Dimitris Bertsimas and John N. Tsitsiklis.

Submitted by: Serkan Hosten

Date: August 2012