**Overview**

Will be updated

**Prerequisite**

MATH 547 or equivalent

**Topics**

- Introduction to mathematical optimization
- Mathematical optimization and fundamental concepts
- Motivating examples and real-world applications

- A review on linear algebra: vectors, matrices, and linear systems
- Linear programming
- Linear programming with two variables
- Forms of linear programming problems, and preprocessing
- Basic solutions and basic feasible solutions

- Simplex methods for linear programming
- Simplex method in matrix form
- Simplex method with tableaux
- Two-phase simplex method

- Duality and sensitivity analysis in linear programming
- Introduction to linear programming software
- Applications of linear programming
- Classical problems
- Engineering applications
- Blending and inventory problems
- Transportation problems
- Minimum cost network flow problems

- Introduction to nonlinear programming
- A review on mathematical tools
- Quadratic programming and its applications
- Convex programming

- Introduction to integer programming (
*if time permits*)