Objectives

This course introduces students to the theory and the algorithms of optimization. Applications to logistics, manufacturing, transportation, resource allocation, modern portfolio theory and machine learning. Exercises and theory are equally important for the success of the class. Some examples are provided in Python.

By the end of this course, the students should be able to :

1. understand optimization methods and the algorithms developed for solving various types of problems,

2. be able to apply these methods and algorithms to problems encountered in management science.

Contents

1. Linear programming

2. Graph theory and networks

3. The shortest path problems

4. The transshipment problem

5. Combinatorial optimization and the Branch and Bound algorithm

6. Dynamic programming and the knapsack problem

7. Non-linear optimization and optimality conditions

8. Lagrange multipliers and duality

9. Conjugate gradient method

10. Quasi-Newton methods

11. Numerical optimization in Python with SciPy

12. Portfolio Optimization

13. Reinforcement learning

References

- Luenberger, D. G., Ye, Y., Linear and Nonlinear Programming, Fourth Edition, Springer, 2016.

- Bierlaire, M., Optimization : Principles and Algorithms, PPUR, 2015.

- Nocedal, J.; Wright, S. J., Numerical Optimization, Second Edition, Springer, 2006.

- Bertsekas, D. P., Dynamic Programming and Optimal Control, Fourth Edition, Springer, 2017.

Pre-requisites

- Linear algebra

- Some basic concepts in multivariate calculus (gradient and hessian of a function)

Evaluation

First attempt

Exam:

Written 2h00 hours

Documentation:

Not allowed

Calculator:

Allowed with restrictions

Evaluation:

Written exam. No documentation. 4 function calculator according to HEC directive.

Retake

Exam:

Written 2h00 hours

Documentation:

Not allowed

Calculator:

Allowed with restrictions

Evaluation:

Written exam. No documentation. 4 function calculator according to HEC directive.