Summary

This course introduces students to continuous, nonlinear optimization. We investigate properties of optimization problems with continuous variables, and we analyze and implement important algorithms to solve constrained and unconstrained problems.

Content

Learning Prerequisites

Required courses

Students are expected to be comfortable with linear algebra, analysis and mathematical proofs.

Students are expected to be comfortable writing simple code in Matlab. They may be allowed to write some of their work in Python or Julia upon request.

Learning Outcomes

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

• Recognize and formulate a mathematical optimization problem.
• Analyze and implement the gradient descent method, Newton's method, the trust-region method and the augmented Lagrangian method, among others.
• Establish and discuss local and global convergence guarantees for iterative algorithms.
• Exploit elementary notions of convexity and duality in optimization.
• Apply the general theory to particular cases.
• Prove some of the most important theorems studied in class.

Teaching methods

 Lectures + exercise sessions

Expected student activities

Students are expected to attend lectures and participate actively in class and exercises. Exercises will include both theoretical work and programming assignments. Students also complete projects that likewise include theoretical and numerical work.

Assessment methods

Final exam (40%) + homework/projects (60%)

Supervision

Resources

Bibliography

Book "Numerical Optimization", J. Nocedal and S. Wright, Springer 2006: https://link.springer.com/book/10.1007/978-0-387-40065-5

Ressources en bibliothèque

• Numerical Optimization / J. Nocedal & S. Wright
• (lien direct Open Access)

Notes/Handbook

Lecture notes provided by the lecturer.