STOR 415: Introduction to Optimization

Overview

Will be updated

Prerequisite

MATH 547 or equivalent

Topics

  1. Introduction to mathematical optimization
    • Mathematical optimization and fundamental concepts
    • Motivating examples and real-world applications
  2. A review on linear algebra: vectors, matrices, and linear systems
  3. Linear programming
    • Linear programming with two variables
    • Forms of linear programming problems, and preprocessing
    • Basic solutions and basic feasible solutions
  4. Simplex methods for linear programming
    • Simplex method in matrix form
    • Simplex method with tableaux
    • Two-phase simplex method
  5. Duality and sensitivity analysis in linear programming
  6. Introduction to linear programming software
  7. Applications of linear programming
    • Classical problems
    • Engineering applications
    • Blending and inventory problems
    • Transportation problems
    • Minimum cost network flow problems
  8. Introduction to nonlinear programming
    • A review on mathematical tools
    • Quadratic programming and its applications
    • Convex programming
  9. Introduction to integer programming (if time permits)