Optimization methods

Summary

This course presents the problem of static optimization, with and without (equality and inequality) constraints, both from the theoretical (optimality conditions) and methodological (algorithms) point of view. Economics and financial applications are provided. Dynamic optimization is also introduced

Content

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Keywords

Optimization program, equality and inequality constraints, Lagrange and Kuhn-Tucker theorems, algorithms, Bellman equation, optimal control.

 

Learning Prerequisites

Important concepts to start the course

Basic concepts of linear algebra, mathematical analysis and probability.

Learning Outcomes

By the end of the course, the student must be able to:

• Describe optimization programs with and without equality or inequality constraints
• Solve optimization programs with and without equality or inequality constraints
• Describe algorithms adopted to solve such a univariate and multivariate optimization problems.
• Apply different algorithm to financial applications such as portfolio optimization and parameter estimation.
• Solve simple optimal control problems.

Transversal skills

• Use a work methodology appropriate to the task.
• Set objectives and design an action plan to reach those objectives.
• Demonstrate the capacity for critical thinking
• Use both general and domain specific IT resources and tools

Teaching methods

Slides.

Assessment methods

The grading will be based on exercises (30%), and (70%) final exam. The final exam is closed-books and closed-notes.

Resources

Virtual desktop infrastructure (VDI)

No

Bibliography

-  Brandimarte P., “ Numerical Methods in Finance”, Wiley Series in Economics and Statistics

- Dixit, A. K., "Optimization in economic theory", Oxford University Press, second edition.

 

- C. P. Simon and L.E. Blume, "Mathematics for Economists", W. W. Norton and Company

- R. K. Sundaram, "A First Course in Optimization Theory", Cambridge University Press.

Ressources en bibliothèque

• A First Course in Optimization Theory / Sundaram
• Mathematics for Economists / Simon
• Optimization in Economic Theory / Dixit
• Numerical Methods in Finance / Brandimarte

Notes/Handbook

Slides for each lectures will be provided.

Moodle Link

• https://go.epfl.ch/FIN-414